%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA170-1 : 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 1.13s 1.34s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA170-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n005.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 00:56:47 EDT 2026
% 0.13/0.33 % CPUTime :
% 1.13/1.34 % SZS status Unsatisfiable
% 1.13/1.34 % SZS output start Proof
% 1.13/1.34 tff(b_type, type, (
% 1.13/1.34 b: ( $i * $i ) > $o)).
% 1.13/1.34 tff(s_type, type, (
% 1.13/1.34 s: $i > $i)).
% 1.13/1.34 tff(z_type, type, (
% 1.13/1.34 z: $i)).
% 1.13/1.34 tff(elem_1_type, type, (
% 1.13/1.34 elem_1: $i)).
% 1.13/1.34 tff(r_type, type, (
% 1.13/1.34 r: ( $i * $i ) > $o)).
% 1.13/1.34 tff(inj_0_type, type, (
% 1.13/1.34 inj_0: $i > $i)).
% 1.13/1.34 tff(1,assumption,(~(s(elem!1) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.34 tff(2,plain,
% 1.13/1.34 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(commutativity,[status(thm)],[])).
% 1.13/1.34 tff(3,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 1.13/1.34 tff(4,plain,
% 1.13/1.34 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[3, 2])).
% 1.13/1.34 tff(5,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1, 4])).
% 1.13/1.34 tff(6,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(7,plain,
% 1.13/1.34 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[6, 1])).
% 1.13/1.34 tff(8,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.13/1.34 tff(9,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(10,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(11,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(12,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.13/1.34 tff(13,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.13/1.34 tff(14,plain,
% 1.13/1.34 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(15,plain,
% 1.13/1.34 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[14])).
% 1.13/1.34 tff(16,plain,
% 1.13/1.34 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(17,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 1.13/1.34 tff(18,plain,
% 1.13/1.34 (![X: $i] : (~(s(X) = z))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.13/1.34 tff(19,plain,(
% 1.13/1.34 ![X: $i] : (~(s(X) = z))),
% 1.13/1.34 inference(skolemize,[status(sab)],[18])).
% 1.13/1.34 tff(20,plain,
% 1.13/1.34 (![X: $i] : (~(s(X) = z))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.13/1.34 tff(21,plain,
% 1.13/1.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(22,plain,
% 1.13/1.34 (~(s(s(s(elem!1))) = z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[21, 20])).
% 1.13/1.34 tff(23,plain,
% 1.13/1.34 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(24,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[23])).
% 1.13/1.34 tff(25,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(26,plain,
% 1.13/1.34 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(27,plain,
% 1.13/1.34 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[26])).
% 1.13/1.34 tff(28,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 1.13/1.34 tff(29,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.13/1.34 tff(30,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.13/1.34 tff(31,plain,(
% 1.13/1.34 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.13/1.34 inference(skolemize,[status(sab)],[30])).
% 1.13/1.34 tff(32,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.13/1.34 tff(33,plain,
% 1.13/1.34 (((~![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))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(34,plain,
% 1.13/1.34 ((~![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))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(35,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[34, 33])).
% 1.13/1.34 tff(36,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[35, 32, 22, 13, 12])).
% 1.13/1.34 tff(37,plain,(r(s(s(s(elem!1))), z) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(38,plain,
% 1.13/1.34 (r(s(s(s(elem!1))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[37, 12])).
% 1.13/1.34 tff(39,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.13/1.34 tff(40,plain,
% 1.13/1.34 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(41,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(42,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(43,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 1.13/1.34 tff(44,plain,
% 1.13/1.34 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.13/1.34 tff(45,plain,(
% 1.13/1.34 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.13/1.34 inference(skolemize,[status(sab)],[44])).
% 1.13/1.34 tff(46,plain,
% 1.13/1.34 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.13/1.34 tff(47,plain,
% 1.13/1.34 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[46, 40])).
% 1.13/1.34 tff(48,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(49,plain,
% 1.13/1.34 (inj_0(s(elem!1)) = elem!1),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[48, 47])).
% 1.13/1.34 tff(50,plain,
% 1.13/1.34 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[39])).
% 1.13/1.34 tff(51,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(52,plain,
% 1.13/1.34 (inj_0(s(z)) = z),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[51, 47])).
% 1.13/1.34 tff(53,plain,
% 1.13/1.34 (z = inj_0(s(z))),
% 1.13/1.34 inference(symmetry,[status(thm)],[52])).
% 1.13/1.34 tff(54,plain,
% 1.13/1.34 (z = elem!1),
% 1.13/1.34 inference(transitivity,[status(thm)],[53, 50, 49])).
% 1.13/1.34 tff(55,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.13/1.34 tff(56,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[55, 54])).
% 1.13/1.34 tff(57,plain,((~(s(z) = s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(58,plain,
% 1.13/1.34 (z = elem!1),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[57, 39])).
% 1.13/1.34 tff(59,plain,
% 1.13/1.34 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[58])).
% 1.13/1.34 tff(60,plain,
% 1.13/1.34 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[59])).
% 1.13/1.34 tff(61,plain,
% 1.13/1.34 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(commutativity,[status(thm)],[])).
% 1.13/1.34 tff(62,plain,
% 1.13/1.34 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[58])).
% 1.13/1.34 tff(63,plain,
% 1.13/1.34 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[62, 61])).
% 1.13/1.34 tff(64,plain,
% 1.13/1.34 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[63])).
% 1.13/1.34 tff(65,plain,
% 1.13/1.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(66,plain,
% 1.13/1.34 (~(s(s(s(s(elem!1)))) = z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[65, 20])).
% 1.13/1.34 tff(67,plain,
% 1.13/1.34 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[66, 64])).
% 1.13/1.34 tff(68,plain,
% 1.13/1.34 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[58])).
% 1.13/1.34 tff(69,plain,
% 1.13/1.34 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 1.13/1.34 inference(symmetry,[status(thm)],[68])).
% 1.13/1.34 tff(70,plain,
% 1.13/1.34 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[69])).
% 1.13/1.34 tff(71,plain,
% 1.13/1.34 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(72,plain,
% 1.13/1.34 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[71])).
% 1.13/1.34 tff(73,plain,
% 1.13/1.34 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(74,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 1.13/1.34 tff(75,plain,
% 1.13/1.34 (![X: $i] : (~b(X, X))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.13/1.34 tff(76,plain,(
% 1.13/1.34 ![X: $i] : (~b(X, X))),
% 1.13/1.34 inference(skolemize,[status(sab)],[75])).
% 1.13/1.34 tff(77,plain,
% 1.13/1.34 (![X: $i] : (~b(X, X))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.13/1.34 tff(78,plain,
% 1.13/1.34 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(79,plain,
% 1.13/1.34 (~b(elem!1, elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[78, 77])).
% 1.13/1.34 tff(80,plain,
% 1.13/1.34 (~b(z, elem!1)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[79, 70])).
% 1.13/1.34 tff(81,plain,
% 1.13/1.34 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[58])).
% 1.13/1.34 tff(82,plain,
% 1.13/1.34 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.13/1.34 inference(symmetry,[status(thm)],[81])).
% 1.13/1.34 tff(83,plain,
% 1.13/1.34 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[82])).
% 1.13/1.34 tff(84,plain,
% 1.13/1.34 (~b(elem!1, z)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[79, 83])).
% 1.13/1.34 tff(85,plain,
% 1.13/1.34 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[58])).
% 1.13/1.34 tff(86,plain,
% 1.13/1.34 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[85])).
% 1.13/1.34 tff(87,plain,
% 1.13/1.34 (~b(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[12, 86])).
% 1.13/1.34 tff(88,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.13/1.34 tff(89,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.13/1.34 tff(90,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.13/1.34 tff(91,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.13/1.34 tff(92,plain,
% 1.13/1.34 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[91])).
% 1.13/1.34 tff(93,plain,
% 1.13/1.34 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[92])).
% 1.13/1.34 tff(94,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1, 93])).
% 1.13/1.34 tff(95,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(96,plain,
% 1.13/1.34 (~(s(s(s(elem!1))) = elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[95, 1])).
% 1.13/1.34 tff(97,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.13/1.34 tff(98,plain,
% 1.13/1.34 (s(s(elem!1)) = s(elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[97])).
% 1.13/1.34 tff(99,plain,
% 1.13/1.34 (s(s(elem!1)) = elem!1),
% 1.13/1.34 inference(transitivity,[status(thm)],[98, 97])).
% 1.13/1.34 tff(100,plain,
% 1.13/1.34 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[99])).
% 1.13/1.34 tff(101,plain,
% 1.13/1.34 (s(s(s(elem!1))) = elem!1),
% 1.13/1.34 inference(transitivity,[status(thm)],[100, 97])).
% 1.13/1.34 tff(102,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.13/1.34 tff(103,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[102, 101])).
% 1.13/1.34 tff(104,plain,((~(s(elem!1) = elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(105,plain,
% 1.13/1.34 (~(s(elem!1) = elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[104, 96])).
% 1.13/1.34 tff(106,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.13/1.34 tff(107,plain,
% 1.13/1.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(108,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(109,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.13/1.34 tff(110,plain,
% 1.13/1.34 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[109, 32])).
% 1.13/1.34 tff(111,plain,
% 1.13/1.34 (r(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[110, 88, 96])).
% 1.13/1.34 tff(112,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(113,plain,
% 1.13/1.34 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[112, 47])).
% 1.13/1.34 tff(114,assumption,(z = elem!1), introduced(assumption)).
% 1.13/1.34 tff(115,plain,
% 1.13/1.34 (s(z) = s(elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[114])).
% 1.13/1.34 tff(116,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[9, 115])).
% 1.13/1.34 tff(117,plain,((~(z = elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(118,plain,
% 1.13/1.34 (~(z = elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[117, 9])).
% 1.13/1.34 tff(119,plain,
% 1.13/1.34 ((elem!1 = z) <=> (z = elem!1)),
% 1.13/1.34 inference(commutativity,[status(thm)],[])).
% 1.13/1.34 tff(120,assumption,(elem!1 = z), introduced(assumption)).
% 1.13/1.34 tff(121,plain,
% 1.13/1.34 (z = elem!1),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.13/1.34 tff(122,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[55, 121])).
% 1.13/1.34 tff(123,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(124,plain,
% 1.13/1.34 (~(elem!1 = z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[123, 118])).
% 1.13/1.34 tff(125,plain,
% 1.13/1.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(126,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(127,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.13/1.34 tff(128,plain,
% 1.13/1.34 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[127, 32])).
% 1.13/1.34 tff(129,plain,
% 1.13/1.34 (r(elem!1, z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[128, 124, 89])).
% 1.13/1.34 tff(130,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.13/1.34 tff(131,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.13/1.34 tff(132,plain,
% 1.13/1.34 (^[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))))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(133,plain,
% 1.13/1.34 (![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)))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[132])).
% 1.13/1.34 tff(134,plain,
% 1.13/1.34 (![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)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(135,plain,
% 1.13/1.34 (^[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))))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(136,plain,
% 1.13/1.34 (![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)))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[135])).
% 1.13/1.34 tff(137,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 1.13/1.34 tff(138,plain,
% 1.13/1.34 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.13/1.34 tff(139,plain,
% 1.13/1.34 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.13/1.34 tff(140,plain,(
% 1.13/1.34 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.34 inference(skolemize,[status(sab)],[139])).
% 1.13/1.34 tff(141,plain,
% 1.13/1.34 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.13/1.34 tff(142,plain,
% 1.13/1.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(143,plain,
% 1.13/1.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(144,plain,
% 1.13/1.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.13/1.34 tff(145,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[144, 141, 131, 130, 106])).
% 1.13/1.34 tff(146,plain,((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(147,plain,
% 1.13/1.34 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[146, 129, 106])).
% 1.13/1.34 tff(148,plain,
% 1.13/1.34 (((~![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))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(149,plain,
% 1.13/1.34 ((~![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))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(150,plain,
% 1.13/1.34 ((~![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)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.13/1.34 tff(151,plain,
% 1.13/1.34 ((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)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[150, 32])).
% 1.13/1.34 tff(152,plain,
% 1.13/1.34 (s(s(s(s(elem!1)))) = elem!1),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[151, 147, 8])).
% 1.13/1.34 tff(153,plain,
% 1.13/1.34 (elem!1 = s(s(s(s(elem!1))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[152])).
% 1.13/1.34 tff(154,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(155,plain,
% 1.13/1.34 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[154, 47])).
% 1.13/1.34 tff(156,plain,
% 1.13/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(157,plain,
% 1.13/1.34 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[156, 47])).
% 1.13/1.34 tff(158,plain,
% 1.13/1.34 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[152])).
% 1.13/1.34 tff(159,plain,
% 1.13/1.34 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[158])).
% 1.13/1.34 tff(160,plain,
% 1.13/1.34 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[159])).
% 1.13/1.34 tff(161,plain,
% 1.13/1.34 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[160])).
% 1.13/1.34 tff(162,plain,
% 1.13/1.34 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[161])).
% 1.13/1.34 tff(163,plain,
% 1.13/1.34 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[162])).
% 1.13/1.34 tff(164,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 1.13/1.34 tff(165,plain,
% 1.13/1.34 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.13/1.34 inference(monotonicity,[status(thm)],[152])).
% 1.13/1.34 tff(166,plain,
% 1.13/1.34 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(symmetry,[status(thm)],[165])).
% 1.13/1.34 tff(167,plain,
% 1.13/1.34 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[166])).
% 1.13/1.34 tff(168,plain,
% 1.13/1.34 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[88, 167])).
% 1.13/1.34 tff(169,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.13/1.34 tff(170,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.13/1.34 tff(171,plain,
% 1.13/1.34 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[152])).
% 1.13/1.34 tff(172,plain,
% 1.13/1.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(173,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(174,plain,
% 1.13/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.13/1.34 tff(175,plain,
% 1.13/1.34 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[174, 32])).
% 1.13/1.34 tff(176,plain,
% 1.13/1.34 (r(z, elem!1)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[175, 118, 90])).
% 1.13/1.34 tff(177,plain,
% 1.13/1.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(178,plain,
% 1.13/1.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(179,plain,
% 1.13/1.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.13/1.34 tff(180,plain,
% 1.13/1.34 (~r(s(s(s(elem!1))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[179, 141, 176, 170])).
% 1.13/1.34 tff(181,plain,
% 1.13/1.34 (b(s(s(s(elem!1))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[37, 180])).
% 1.13/1.34 tff(182,plain,
% 1.13/1.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(183,plain,
% 1.13/1.34 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(184,plain,
% 1.13/1.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[183])).
% 1.13/1.34 tff(185,plain,
% 1.13/1.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[184, 182])).
% 1.13/1.35 tff(186,plain,
% 1.13/1.35 ((~![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))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(187,plain,
% 1.13/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.13/1.35 tff(188,plain,
% 1.13/1.35 (~r(z, s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[187, 141, 176, 170])).
% 1.13/1.35 tff(189,plain,
% 1.13/1.35 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.13/1.35 inference(commutativity,[status(thm)],[])).
% 1.13/1.35 tff(190,plain,
% 1.13/1.35 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[189])).
% 1.13/1.35 tff(191,plain,
% 1.13/1.35 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[190])).
% 1.13/1.35 tff(192,plain,
% 1.13/1.35 (~(z = s(s(s(elem!1))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[22, 191])).
% 1.13/1.35 tff(193,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(194,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(195,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.13/1.35 tff(196,plain,
% 1.13/1.35 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[195, 32])).
% 1.13/1.35 tff(197,plain,
% 1.13/1.35 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[196, 192])).
% 1.13/1.35 tff(198,plain,
% 1.13/1.35 (b(z, s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[197, 188])).
% 1.13/1.35 tff(199,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.13/1.35 tff(200,plain,
% 1.13/1.35 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.35 tff(201,plain,
% 1.13/1.35 (b(elem!1, s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.35 inference(symmetry,[status(thm)],[200])).
% 1.13/1.35 tff(202,plain,
% 1.13/1.35 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.35 tff(203,plain,
% 1.13/1.35 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[202])).
% 1.13/1.35 tff(204,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.13/1.35 tff(205,plain,
% 1.13/1.35 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[204])).
% 1.13/1.35 tff(206,plain,
% 1.13/1.35 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[113])).
% 1.13/1.35 tff(207,plain,
% 1.13/1.35 (s(s(s(elem!1))) = z),
% 1.13/1.35 inference(transitivity,[status(thm)],[206, 205, 52])).
% 1.13/1.35 tff(208,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[22, 207])).
% 1.13/1.35 tff(209,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(210,plain,
% 1.13/1.35 (~(elem!1 = s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[209, 203])).
% 1.13/1.35 tff(211,assumption,(~b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.13/1.35 tff(212,assumption,(~r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.13/1.35 tff(213,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(214,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(215,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.13/1.35 tff(216,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[215, 32, 212, 211, 209])).
% 1.13/1.35 tff(217,plain,(b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(218,plain,
% 1.13/1.35 (r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[217, 211])).
% 1.13/1.35 tff(219,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.13/1.35 tff(220,assumption,(r(s(z), z)), introduced(assumption)).
% 1.13/1.35 tff(221,plain,
% 1.13/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(222,plain,
% 1.13/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(223,plain,
% 1.13/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[222, 221])).
% 1.13/1.35 tff(224,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[223, 141, 220, 106, 219])).
% 1.13/1.35 tff(225,plain,((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(226,plain,
% 1.13/1.35 (~r(s(z), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[225, 218, 106])).
% 1.13/1.35 tff(227,plain,
% 1.13/1.35 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(228,plain,
% 1.13/1.35 (~(s(z) = z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[227, 20])).
% 1.13/1.35 tff(229,plain,
% 1.13/1.35 (((~![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))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(230,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(231,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.13/1.35 tff(232,plain,
% 1.13/1.35 (b(s(z), z) | r(s(z), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[231, 32, 228])).
% 1.13/1.35 tff(233,plain,
% 1.13/1.35 (b(s(z), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[232, 226])).
% 1.13/1.35 tff(234,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.13/1.35 tff(235,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.35 tff(236,plain,
% 1.13/1.35 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(237,plain,
% 1.13/1.35 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[236])).
% 1.13/1.35 tff(238,plain,
% 1.13/1.35 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(239,plain,
% 1.13/1.35 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))) <=> ((~b(X0, 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(X0, X4))) <=> ((~b(X0, 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(X0, X4))) | (~b(X3, X4))) <=> (((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X0, 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(X0, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(240,plain,
% 1.13/1.35 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[239])).
% 1.13/1.35 tff(241,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 1.13/1.35 tff(242,plain,
% 1.13/1.35 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.13/1.35 tff(243,plain,
% 1.13/1.35 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[242, 238])).
% 1.13/1.35 tff(244,plain,(
% 1.13/1.35 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.35 inference(skolemize,[status(sab)],[243])).
% 1.13/1.35 tff(245,plain,
% 1.13/1.35 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[244, 237])).
% 1.13/1.35 tff(246,plain,
% 1.13/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(247,plain,
% 1.13/1.35 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(248,plain,
% 1.13/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[247])).
% 1.13/1.35 tff(249,plain,
% 1.13/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[248, 246])).
% 1.13/1.35 tff(250,plain,
% 1.13/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(251,plain,
% 1.13/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.13/1.35 tff(252,plain,
% 1.13/1.35 (~b(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[251, 245, 235, 234, 233])).
% 1.13/1.35 tff(253,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.13/1.35 tff(254,plain,
% 1.13/1.35 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[253])).
% 1.13/1.35 tff(255,plain,
% 1.13/1.35 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[157])).
% 1.13/1.35 tff(256,plain,
% 1.13/1.35 (s(s(elem!1)) = z),
% 1.13/1.35 inference(transitivity,[status(thm)],[255, 254, 52])).
% 1.13/1.35 tff(257,plain,
% 1.13/1.35 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(258,plain,
% 1.13/1.35 (~(s(s(elem!1)) = z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[257, 20])).
% 1.13/1.35 tff(259,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[258, 256])).
% 1.13/1.35 tff(260,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(261,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(262,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(263,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.13/1.35 tff(264,plain,
% 1.13/1.35 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[263, 32])).
% 1.13/1.35 tff(265,plain,
% 1.13/1.35 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[264, 260])).
% 1.13/1.35 tff(266,plain,
% 1.13/1.35 (r(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[265, 252])).
% 1.13/1.35 tff(267,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.13/1.35 tff(268,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.13/1.35 tff(269,plain,
% 1.13/1.35 (((~![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(elem!1))), 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(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(270,plain,
% 1.13/1.35 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(271,plain,
% 1.13/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[270])).
% 1.13/1.35 tff(272,plain,
% 1.13/1.35 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[271, 269])).
% 1.13/1.35 tff(273,plain,
% 1.13/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(274,plain,
% 1.13/1.35 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[273, 272])).
% 1.13/1.35 tff(275,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[274, 141, 268, 170, 267])).
% 1.13/1.35 tff(276,plain,((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(277,plain,
% 1.13/1.35 (~r(elem!1, s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[276, 266, 170])).
% 1.13/1.35 tff(278,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(279,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(280,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[279, 278])).
% 1.13/1.35 tff(281,plain,
% 1.13/1.35 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[280, 32])).
% 1.13/1.35 tff(282,plain,
% 1.13/1.35 (b(elem!1, s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[281, 277, 210])).
% 1.13/1.35 tff(283,plain,
% 1.13/1.35 (b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[282, 201])).
% 1.13/1.35 tff(284,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[211, 283])).
% 1.13/1.35 tff(285,plain,(b(s(s(s(s(elem!1)))), s(z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(286,plain,
% 1.13/1.35 (b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[285, 152, 170, 198, 181, 106])).
% 1.13/1.35 tff(287,plain,
% 1.13/1.35 (b(elem!1, s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[286, 171])).
% 1.13/1.35 tff(288,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.13/1.35 tff(289,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.13/1.35 tff(290,plain,
% 1.13/1.35 (~r(s(s(s(elem!1))), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[179, 141, 289, 170])).
% 1.13/1.35 tff(291,plain,
% 1.13/1.35 (b(s(s(s(elem!1))), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[37, 290])).
% 1.13/1.35 tff(292,plain,
% 1.13/1.35 (~r(z, s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[187, 141, 289, 170])).
% 1.13/1.35 tff(293,plain,
% 1.13/1.35 (b(z, s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[197, 292])).
% 1.13/1.35 tff(294,plain,
% 1.13/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(295,plain,
% 1.13/1.35 (((~b(s(s(s(elem!1))), z)) | (~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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(296,plain,
% 1.13/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), 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(X0, 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(s(elem!1))), s(elem!1)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[295])).
% 1.13/1.35 tff(297,plain,
% 1.13/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), 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(X0, 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(s(elem!1))), s(elem!1))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[296, 294])).
% 1.13/1.35 tff(298,plain,
% 1.13/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), 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))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(299,plain,
% 1.13/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.13/1.35 tff(300,plain,
% 1.13/1.35 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[299, 245, 293, 291, 288])).
% 1.13/1.35 tff(301,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.13/1.35 tff(302,plain,
% 1.13/1.35 (r(z, s(s(s(s(elem!1))))) <=> r(z, elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.35 tff(303,plain,
% 1.13/1.35 (r(z, elem!1) <=> r(z, s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[302])).
% 1.13/1.35 tff(304,plain,
% 1.13/1.35 (r(z, s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[289, 303])).
% 1.13/1.35 tff(305,assumption,(~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.35 tff(306,plain,
% 1.13/1.35 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.35 tff(307,plain,
% 1.13/1.35 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[306])).
% 1.13/1.35 tff(308,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.13/1.35 tff(309,plain,
% 1.13/1.35 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[308, 307])).
% 1.13/1.35 tff(310,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.35 tff(311,plain,
% 1.13/1.35 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.35 tff(312,plain,
% 1.13/1.35 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[311])).
% 1.13/1.35 tff(313,plain,
% 1.13/1.35 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[312])).
% 1.13/1.35 tff(314,plain,
% 1.13/1.35 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[313])).
% 1.13/1.35 tff(315,plain,
% 1.13/1.35 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.13/1.35 inference(symmetry,[status(thm)],[314])).
% 1.13/1.35 tff(316,plain,
% 1.13/1.35 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.35 tff(317,plain,
% 1.13/1.35 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(318,plain,
% 1.13/1.35 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[317, 47])).
% 1.13/1.35 tff(319,plain,
% 1.13/1.35 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(320,plain,
% 1.13/1.35 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[319, 47])).
% 1.13/1.35 tff(321,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.35 tff(322,plain,
% 1.13/1.35 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[321])).
% 1.13/1.35 tff(323,plain,
% 1.13/1.35 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[322])).
% 1.13/1.35 tff(324,plain,
% 1.13/1.35 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[206, 323, 320])).
% 1.13/1.35 tff(325,plain,
% 1.13/1.35 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[324])).
% 1.13/1.35 tff(326,plain,
% 1.13/1.35 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[255, 325, 318])).
% 1.13/1.35 tff(327,plain,
% 1.13/1.35 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[326])).
% 1.13/1.35 tff(328,plain,
% 1.13/1.35 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.13/1.35 inference(symmetry,[status(thm)],[327])).
% 1.13/1.35 tff(329,plain,
% 1.13/1.35 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.35 inference(transitivity,[status(thm)],[206, 328, 155])).
% 1.13/1.35 tff(330,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[11, 329])).
% 1.13/1.35 tff(331,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(332,plain,
% 1.13/1.35 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[331, 11])).
% 1.13/1.35 tff(333,plain,
% 1.13/1.35 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.35 tff(334,plain,
% 1.13/1.35 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[333])).
% 1.13/1.35 tff(335,plain,
% 1.13/1.35 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[313])).
% 1.13/1.35 tff(336,plain,
% 1.13/1.35 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[335, 334])).
% 1.13/1.35 tff(337,plain,
% 1.13/1.35 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[336])).
% 1.13/1.35 tff(338,plain,
% 1.13/1.35 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.13/1.35 inference(commutativity,[status(thm)],[])).
% 1.13/1.35 tff(339,plain,
% 1.13/1.35 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.13/1.35 inference(symmetry,[status(thm)],[338])).
% 1.13/1.35 tff(340,plain,
% 1.13/1.35 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.13/1.35 inference(transitivity,[status(thm)],[202, 339])).
% 1.13/1.35 tff(341,plain,
% 1.13/1.35 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[340])).
% 1.13/1.35 tff(342,plain,
% 1.13/1.35 (~(s(z) = elem!1)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[209, 341])).
% 1.13/1.35 tff(343,plain,
% 1.13/1.35 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.13/1.35 inference(commutativity,[status(thm)],[])).
% 1.13/1.36 tff(344,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.13/1.36 tff(345,plain,
% 1.13/1.36 (s(z) = s(elem!1)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.13/1.36 tff(346,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[9, 345])).
% 1.13/1.36 tff(347,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(348,plain,
% 1.13/1.36 (~(s(elem!1) = s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[347, 9])).
% 1.13/1.36 tff(349,plain,
% 1.13/1.36 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[299, 245, 235, 234, 288])).
% 1.13/1.36 tff(350,plain,
% 1.13/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(351,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(352,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.13/1.36 tff(353,plain,
% 1.13/1.36 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[352, 32])).
% 1.13/1.36 tff(354,plain,
% 1.13/1.36 (r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[353, 11, 349])).
% 1.13/1.36 tff(355,assumption,(b(s(z), z)), introduced(assumption)).
% 1.13/1.36 tff(356,plain,
% 1.13/1.36 (~b(s(s(s(elem!1))), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[251, 245, 235, 234, 355])).
% 1.13/1.36 tff(357,plain,
% 1.13/1.36 (r(s(s(s(elem!1))), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[265, 356])).
% 1.13/1.36 tff(358,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.13/1.36 tff(359,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), z)) | (~b(s(elem!1), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(360,plain,
% 1.13/1.36 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(361,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(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(X0, 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(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[360])).
% 1.13/1.36 tff(362,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(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(X0, 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(z), z)) | (~b(s(elem!1), s(z))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[361, 359])).
% 1.13/1.36 tff(363,plain,
% 1.13/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(364,plain,
% 1.13/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), z)) | (~b(s(elem!1), s(z)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[363, 362])).
% 1.13/1.36 tff(365,plain,
% 1.13/1.36 (~b(s(elem!1), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[364, 245, 235, 234, 355, 288])).
% 1.13/1.36 tff(366,plain,
% 1.13/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(367,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(368,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[367, 366])).
% 1.13/1.36 tff(369,plain,
% 1.13/1.36 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[368, 32])).
% 1.13/1.36 tff(370,plain,
% 1.13/1.36 (r(s(elem!1), s(z))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[369, 365, 358])).
% 1.13/1.36 tff(371,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(372,plain,
% 1.13/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(373,plain,
% 1.13/1.36 (((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(374,plain,
% 1.13/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[373])).
% 1.13/1.36 tff(375,plain,
% 1.13/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[374, 372])).
% 1.13/1.36 tff(376,plain,
% 1.13/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(377,plain,
% 1.13/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.13/1.36 tff(378,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[377, 141, 371, 370, 357])).
% 1.13/1.36 tff(379,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(380,plain,
% 1.13/1.36 (~b(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[379, 354, 348, 235, 234, 288])).
% 1.13/1.36 tff(381,plain,
% 1.13/1.36 (r(s(z), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[232, 380])).
% 1.13/1.36 tff(382,plain,
% 1.13/1.36 (((~![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)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(383,plain,
% 1.13/1.36 ((~![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)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(384,plain,
% 1.13/1.36 ((~![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))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.13/1.36 tff(385,plain,
% 1.13/1.36 (~r(s(z), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[384, 141, 131, 381])).
% 1.13/1.36 tff(386,plain,
% 1.13/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(387,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(388,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.13/1.36 tff(389,plain,
% 1.13/1.36 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[388, 32])).
% 1.13/1.36 tff(390,plain,
% 1.13/1.36 (b(s(z), elem!1)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[389, 385, 342])).
% 1.13/1.36 tff(391,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(392,plain,
% 1.13/1.36 (s(s(elem!1)) = s(elem!1)),
% 1.13/1.36 inference(symmetry,[status(thm)],[391])).
% 1.13/1.36 tff(393,plain,
% 1.13/1.36 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[392])).
% 1.13/1.36 tff(394,plain,
% 1.13/1.36 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.36 inference(transitivity,[status(thm)],[393, 392])).
% 1.13/1.36 tff(395,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[11, 394])).
% 1.13/1.36 tff(396,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(397,plain,
% 1.13/1.36 (~(s(elem!1) = s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[396, 11])).
% 1.13/1.36 tff(398,plain,
% 1.13/1.36 (elem!1 = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[199, 61])).
% 1.13/1.36 tff(399,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.36 tff(400,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[399, 398])).
% 1.13/1.36 tff(401,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(402,plain,
% 1.13/1.36 (elem!1 = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[401, 199])).
% 1.13/1.36 tff(403,plain,
% 1.13/1.36 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[199])).
% 1.13/1.36 tff(404,plain,
% 1.13/1.36 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[403])).
% 1.13/1.36 tff(405,plain,
% 1.13/1.36 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[170, 404])).
% 1.13/1.36 tff(406,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(407,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.36 tff(408,plain,
% 1.13/1.36 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(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(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(409,plain,
% 1.13/1.36 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(410,plain,
% 1.13/1.36 (((~![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(elem!1))), s(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(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[409])).
% 1.13/1.36 tff(411,plain,
% 1.13/1.36 (((~![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(elem!1))), s(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(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[410, 408])).
% 1.13/1.36 tff(412,plain,
% 1.13/1.36 ((~![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(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(413,plain,
% 1.13/1.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.13/1.36 tff(414,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[413, 141, 371, 407, 406])).
% 1.13/1.36 tff(415,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(416,plain,
% 1.13/1.36 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[415, 354, 405])).
% 1.13/1.36 tff(417,plain,
% 1.13/1.36 (((~![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)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(418,plain,
% 1.13/1.36 ((~![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)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(419,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.13/1.36 tff(420,plain,
% 1.13/1.36 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[419, 32])).
% 1.13/1.36 tff(421,plain,
% 1.13/1.36 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[420, 416, 164])).
% 1.13/1.36 tff(422,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.36 tff(423,plain,
% 1.13/1.36 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[422])).
% 1.13/1.36 tff(424,plain,
% 1.13/1.36 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.13/1.36 inference(symmetry,[status(thm)],[423])).
% 1.13/1.36 tff(425,plain,
% 1.13/1.36 (b(elem!1, s(elem!1))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[10, 424])).
% 1.13/1.36 tff(426,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(427,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[426, 425])).
% 1.13/1.36 tff(428,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | b(elem!1, s(elem!1)) | (~(elem!1 = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(429,plain,
% 1.13/1.36 (b(elem!1, s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[428, 421, 402])).
% 1.13/1.36 tff(430,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(431,plain,
% 1.13/1.36 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(432,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, 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), s(elem!1))) | (~b(s(z), elem!1))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[431])).
% 1.13/1.36 tff(433,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, 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), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[432, 430])).
% 1.13/1.36 tff(434,plain,
% 1.13/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(435,plain,
% 1.13/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), elem!1))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.13/1.36 tff(436,plain,
% 1.13/1.36 (~b(s(z), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[435, 245, 308, 429, 390])).
% 1.13/1.36 tff(437,plain,
% 1.13/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(438,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(439,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[438, 437])).
% 1.13/1.36 tff(440,plain,
% 1.13/1.36 ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[439, 32])).
% 1.13/1.36 tff(441,plain,
% 1.13/1.36 (r(s(z), s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[440, 436, 9])).
% 1.13/1.36 tff(442,plain,
% 1.13/1.36 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[313])).
% 1.13/1.36 tff(443,plain,
% 1.13/1.36 (r(s(z), s(s(s(s(s(s(elem!1))))))) <=> r(s(z), s(s(elem!1)))),
% 1.13/1.36 inference(symmetry,[status(thm)],[442])).
% 1.13/1.36 tff(444,plain,
% 1.13/1.36 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[313])).
% 1.13/1.36 tff(445,plain,
% 1.13/1.36 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[444])).
% 1.13/1.36 tff(446,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.13/1.36 tff(447,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.13/1.36 tff(448,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(449,plain,
% 1.13/1.36 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(450,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[449])).
% 1.13/1.36 tff(451,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[450, 448])).
% 1.13/1.36 tff(452,plain,
% 1.13/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(453,plain,
% 1.13/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[452, 451])).
% 1.13/1.36 tff(454,plain,
% 1.13/1.36 ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[453, 245, 301, 447])).
% 1.13/1.36 tff(455,plain,
% 1.13/1.36 (~b(s(z), s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[454, 446])).
% 1.13/1.36 tff(456,plain,
% 1.13/1.36 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[455, 445])).
% 1.13/1.36 tff(457,assumption,(s(z) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.13/1.36 tff(458,plain,
% 1.13/1.36 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[457])).
% 1.13/1.36 tff(459,plain,
% 1.13/1.36 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 1.13/1.36 inference(symmetry,[status(thm)],[458])).
% 1.13/1.36 tff(460,plain,
% 1.13/1.36 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[320])).
% 1.13/1.36 tff(461,plain,
% 1.13/1.36 (s(s(s(s(s(elem!1))))) = z),
% 1.13/1.36 inference(transitivity,[status(thm)],[460, 459, 52])).
% 1.13/1.36 tff(462,plain,
% 1.13/1.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(463,plain,
% 1.13/1.36 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[462, 20])).
% 1.13/1.36 tff(464,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[463, 461])).
% 1.13/1.36 tff(465,plain,(~(s(z) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(466,plain,
% 1.13/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(467,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(468,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.13/1.36 tff(469,plain,
% 1.13/1.36 ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[468, 32])).
% 1.13/1.36 tff(470,plain,
% 1.13/1.36 (b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[469, 465])).
% 1.13/1.36 tff(471,plain,
% 1.13/1.36 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[470, 456])).
% 1.13/1.36 tff(472,plain,
% 1.13/1.36 (r(s(z), s(s(elem!1)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[471, 443])).
% 1.13/1.36 tff(473,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(474,plain,
% 1.13/1.36 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(475,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[474])).
% 1.13/1.36 tff(476,plain,
% 1.13/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[475, 473])).
% 1.13/1.36 tff(477,plain,
% 1.13/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(478,plain,
% 1.13/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.13/1.37 tff(479,plain,
% 1.13/1.37 ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[478, 245, 301, 308, 447])).
% 1.13/1.37 tff(480,plain,
% 1.13/1.37 (~b(s(elem!1), s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[479, 446])).
% 1.13/1.37 tff(481,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.37 tff(482,plain,
% 1.13/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(483,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(484,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.13/1.37 tff(485,plain,
% 1.13/1.37 (r(s(elem!1), s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[484, 32, 481, 480])).
% 1.13/1.37 tff(486,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.13/1.37 tff(487,plain,
% 1.13/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), 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(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(488,plain,
% 1.13/1.37 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(489,plain,
% 1.13/1.37 (((~![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(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(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[488])).
% 1.13/1.37 tff(490,plain,
% 1.13/1.37 (((~![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(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(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[489, 487])).
% 1.13/1.37 tff(491,plain,
% 1.13/1.37 ((~![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(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(492,plain,
% 1.13/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.13/1.37 tff(493,plain,
% 1.13/1.37 (~r(s(z), s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[492, 141, 486, 485])).
% 1.13/1.37 tff(494,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[493, 472])).
% 1.13/1.37 tff(495,plain,((~b(s(s(elem!1)), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(z), s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(496,plain,
% 1.13/1.37 (~b(s(s(elem!1)), elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[495, 441, 199, 397, 301, 390, 308])).
% 1.13/1.37 tff(497,plain,
% 1.13/1.37 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[496, 337])).
% 1.13/1.37 tff(498,plain,
% 1.13/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(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(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(499,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(500,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.13/1.37 tff(501,plain,
% 1.13/1.37 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[500, 32])).
% 1.13/1.37 tff(502,plain,
% 1.13/1.37 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[501, 497, 332])).
% 1.13/1.37 tff(503,plain,
% 1.13/1.37 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[502, 316])).
% 1.13/1.37 tff(504,plain,
% 1.13/1.37 (r(s(s(elem!1)), elem!1)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[503, 315])).
% 1.13/1.37 tff(505,plain,
% 1.13/1.37 (((~![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)), 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(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(506,plain,
% 1.13/1.37 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(507,plain,
% 1.13/1.37 (((~![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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[506])).
% 1.13/1.37 tff(508,plain,
% 1.13/1.37 (((~![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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.13/1.37 inference(transitivity,[status(thm)],[507, 505])).
% 1.13/1.37 tff(509,plain,
% 1.13/1.37 ((~![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))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(510,plain,
% 1.13/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.13/1.37 tff(511,plain,
% 1.13/1.37 ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[510, 141, 170])).
% 1.13/1.37 tff(512,plain,
% 1.13/1.37 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[511, 504])).
% 1.13/1.37 tff(513,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.37 tff(514,plain,
% 1.13/1.37 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[513])).
% 1.13/1.37 tff(515,plain,
% 1.13/1.37 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.13/1.37 inference(symmetry,[status(thm)],[514])).
% 1.13/1.37 tff(516,plain,
% 1.13/1.37 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.13/1.37 inference(symmetry,[status(thm)],[513])).
% 1.13/1.37 tff(517,plain,
% 1.13/1.37 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.37 inference(transitivity,[status(thm)],[516, 255, 515, 155])).
% 1.13/1.37 tff(518,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[11, 517])).
% 1.13/1.37 tff(519,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(520,plain,
% 1.13/1.37 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[519, 11])).
% 1.13/1.37 tff(521,plain,
% 1.13/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(522,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(523,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[522, 521])).
% 1.13/1.37 tff(524,plain,
% 1.13/1.37 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[523, 32, 520, 512])).
% 1.13/1.37 tff(525,plain,
% 1.13/1.37 (r(s(s(elem!1)), z) <=> r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.13/1.37 inference(monotonicity,[status(thm)],[313])).
% 1.13/1.37 tff(526,plain,
% 1.13/1.37 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(s(s(elem!1)), z)),
% 1.13/1.37 inference(symmetry,[status(thm)],[525])).
% 1.13/1.37 tff(527,plain,
% 1.13/1.37 ((~r(s(s(s(s(s(s(elem!1)))))), z)) <=> (~r(s(s(elem!1)), z))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[526])).
% 1.13/1.37 tff(528,assumption,(r(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 1.13/1.37 tff(529,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.37 tff(530,plain,
% 1.13/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(531,plain,
% 1.13/1.37 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(532,plain,
% 1.13/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(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, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[531])).
% 1.13/1.37 tff(533,plain,
% 1.13/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(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, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[532, 530])).
% 1.13/1.37 tff(534,plain,
% 1.13/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(535,plain,
% 1.13/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.13/1.37 tff(536,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[535, 141, 310, 529, 528])).
% 1.13/1.37 tff(537,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(538,plain,
% 1.13/1.37 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[537, 502, 310])).
% 1.13/1.37 tff(539,plain,
% 1.13/1.37 (~r(s(s(elem!1)), z)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[538, 527])).
% 1.13/1.37 tff(540,plain,
% 1.13/1.37 (((~![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))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(541,plain,
% 1.13/1.37 ((~![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))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(542,plain,
% 1.13/1.37 ((~![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)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.13/1.37 tff(543,plain,
% 1.13/1.37 (b(s(s(elem!1)), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[542, 32, 258, 539])).
% 1.13/1.37 tff(544,plain,
% 1.13/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(545,plain,
% 1.13/1.37 (((~b(s(s(s(elem!1))), z)) | (~b(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))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(546,plain,
% 1.13/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(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(X0, 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)))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[545])).
% 1.13/1.37 tff(547,plain,
% 1.13/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(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(X0, 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))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[546, 544])).
% 1.13/1.37 tff(548,plain,
% 1.13/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(549,plain,
% 1.13/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[548, 547])).
% 1.13/1.37 tff(550,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[549, 245, 235, 234, 543, 524])).
% 1.13/1.37 tff(551,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), z)) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(552,plain,
% 1.13/1.37 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[551, 308, 234, 170, 199, 310, 301, 235, 9, 131, 288, 164])).
% 1.13/1.37 tff(553,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.13/1.37 tff(554,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[553])).
% 1.13/1.37 tff(555,plain,
% 1.13/1.37 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[554])).
% 1.13/1.37 tff(556,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.37 tff(557,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.13/1.37 tff(558,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[305, 557])).
% 1.13/1.37 tff(559,plain,((~(s(s(s(elem!1))) = s(elem!1))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(560,plain,
% 1.13/1.37 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[559, 552, 305])).
% 1.13/1.37 tff(561,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[560, 309])).
% 1.13/1.37 tff(562,plain,((~b(s(elem!1), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), z)) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(563,plain,
% 1.13/1.37 (~b(s(elem!1), elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[562, 288, 305, 291, 170, 304, 301, 293, 9, 131, 199, 164])).
% 1.13/1.37 tff(564,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.13/1.37 tff(565,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.13/1.37 tff(566,plain,
% 1.13/1.37 (((~![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))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(567,plain,
% 1.13/1.37 ((~![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))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(568,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.13/1.37 tff(569,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[568, 32, 565, 564, 169])).
% 1.13/1.37 tff(570,plain,(b(s(elem!1), elem!1) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(571,plain,
% 1.13/1.37 (r(s(elem!1), elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[570, 563, 169])).
% 1.13/1.37 tff(572,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.13/1.37 tff(573,plain,
% 1.13/1.37 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(574,plain,
% 1.13/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(575,plain,
% 1.13/1.37 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.13/1.37 tff(576,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[575, 141, 371, 572, 170])).
% 1.13/1.37 tff(577,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(578,plain,
% 1.13/1.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[577, 571, 170])).
% 1.13/1.37 tff(579,plain,
% 1.13/1.37 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[353, 578, 300])).
% 1.13/1.37 tff(580,plain,
% 1.13/1.37 (elem!1 = s(s(s(s(elem!1))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[199])).
% 1.13/1.37 tff(581,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 1.13/1.37 tff(582,plain,
% 1.13/1.37 (s(s(s(z))) = s(elem!1)),
% 1.13/1.37 inference(symmetry,[status(thm)],[581])).
% 1.13/1.37 tff(583,plain,
% 1.13/1.37 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[582])).
% 1.13/1.37 tff(584,plain,
% 1.13/1.37 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(585,plain,
% 1.13/1.37 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[584, 47])).
% 1.13/1.37 tff(586,plain,
% 1.13/1.37 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[585])).
% 1.13/1.37 tff(587,plain,
% 1.13/1.37 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[586, 583, 49, 580])).
% 1.13/1.37 tff(588,plain,
% 1.13/1.37 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[587])).
% 1.13/1.37 tff(589,plain,
% 1.13/1.37 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(590,plain,
% 1.13/1.37 (inj_0(s(s(z))) = s(z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[589, 47])).
% 1.13/1.37 tff(591,plain,
% 1.13/1.37 (s(z) = inj_0(s(s(z)))),
% 1.13/1.37 inference(symmetry,[status(thm)],[590])).
% 1.13/1.37 tff(592,plain,
% 1.13/1.37 (s(z) = s(elem!1)),
% 1.13/1.37 inference(transitivity,[status(thm)],[591, 588, 113, 553])).
% 1.13/1.37 tff(593,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[9, 592])).
% 1.13/1.37 tff(594,plain,((~(s(elem!1) = s(s(s(z))))) | (s(z) = s(elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(595,plain,
% 1.13/1.37 (~(s(elem!1) = s(s(s(z))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[594, 579, 199, 9])).
% 1.13/1.37 tff(596,plain,
% 1.13/1.37 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(597,plain,
% 1.13/1.37 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[596, 47])).
% 1.13/1.37 tff(598,plain,
% 1.13/1.37 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[312])).
% 1.13/1.37 tff(599,assumption,(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.13/1.37 tff(600,plain,
% 1.13/1.37 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.13/1.37 inference(transitivity,[status(thm)],[599, 598, 553])).
% 1.13/1.37 tff(601,plain,
% 1.13/1.37 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[600])).
% 1.13/1.37 tff(602,plain,
% 1.13/1.37 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(603,plain,
% 1.13/1.38 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[602, 47])).
% 1.13/1.38 tff(604,plain,
% 1.13/1.38 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[603])).
% 1.13/1.38 tff(605,plain,
% 1.13/1.38 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[604, 601, 49, 580])).
% 1.13/1.38 tff(606,plain,
% 1.13/1.38 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[605])).
% 1.13/1.38 tff(607,plain,
% 1.13/1.38 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[606])).
% 1.13/1.38 tff(608,plain,
% 1.13/1.38 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.38 inference(symmetry,[status(thm)],[553])).
% 1.13/1.38 tff(609,plain,
% 1.13/1.38 (s(elem!1) = s(s(s(z)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[608, 206, 607, 597])).
% 1.13/1.38 tff(610,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.13/1.38 tff(611,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[610, 609])).
% 1.13/1.38 tff(612,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))) | (s(elem!1) = s(s(s(z)))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(613,plain,
% 1.13/1.38 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[612, 579, 199, 595])).
% 1.13/1.38 tff(614,plain,
% 1.13/1.38 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[598])).
% 1.13/1.38 tff(615,plain,
% 1.13/1.38 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.38 inference(symmetry,[status(thm)],[579])).
% 1.13/1.38 tff(616,plain,
% 1.13/1.38 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[615, 614])).
% 1.13/1.38 tff(617,plain,
% 1.13/1.38 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[616])).
% 1.13/1.38 tff(618,plain,
% 1.13/1.38 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[617])).
% 1.13/1.38 tff(619,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.13/1.38 tff(620,plain,
% 1.13/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(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))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(621,plain,
% 1.13/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(622,plain,
% 1.13/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[621, 620])).
% 1.13/1.38 tff(623,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[622, 141, 572, 486, 619])).
% 1.13/1.38 tff(624,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(625,plain,
% 1.13/1.38 (~r(s(z), s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[624, 619, 572])).
% 1.13/1.38 tff(626,plain,
% 1.13/1.38 (b(s(z), s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[440, 625, 9])).
% 1.13/1.38 tff(627,plain,
% 1.13/1.38 (((~![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)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(628,plain,
% 1.13/1.38 (((~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)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(629,plain,
% 1.13/1.38 (((~![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))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[628])).
% 1.13/1.38 tff(630,plain,
% 1.13/1.38 (((~![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)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[629, 627])).
% 1.13/1.38 tff(631,plain,
% 1.13/1.38 ((~![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))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(632,plain,
% 1.13/1.38 ((~![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))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.13/1.38 tff(633,plain,
% 1.13/1.38 (~r(z, s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[632, 141, 289, 572])).
% 1.13/1.38 tff(634,plain,
% 1.13/1.38 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.13/1.38 inference(commutativity,[status(thm)],[])).
% 1.13/1.38 tff(635,plain,
% 1.13/1.38 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.13/1.38 inference(symmetry,[status(thm)],[634])).
% 1.13/1.38 tff(636,plain,
% 1.13/1.38 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[635])).
% 1.13/1.38 tff(637,plain,
% 1.13/1.38 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(638,plain,
% 1.13/1.38 (~(s(elem!1) = z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[637, 20])).
% 1.13/1.38 tff(639,plain,
% 1.13/1.38 (~(z = s(elem!1))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[638, 636])).
% 1.13/1.38 tff(640,plain,
% 1.13/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(641,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(642,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[641, 640])).
% 1.13/1.38 tff(643,plain,
% 1.13/1.38 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[642, 32])).
% 1.13/1.38 tff(644,plain,
% 1.13/1.38 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[643, 639])).
% 1.13/1.38 tff(645,plain,
% 1.13/1.38 (b(z, s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[644, 633])).
% 1.13/1.38 tff(646,plain,
% 1.13/1.38 (((~![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)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(647,plain,
% 1.13/1.38 ((~![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)))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(648,plain,
% 1.13/1.38 ((~![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))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.13/1.38 tff(649,plain,
% 1.13/1.38 ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[648, 141])).
% 1.13/1.38 tff(650,plain,
% 1.13/1.38 (~r(s(elem!1), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[649, 572, 289])).
% 1.13/1.38 tff(651,plain,
% 1.13/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(652,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(653,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[652, 651])).
% 1.13/1.38 tff(654,plain,
% 1.13/1.38 (b(s(elem!1), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[653, 32, 638, 650])).
% 1.13/1.38 tff(655,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.13/1.38 tff(656,plain,
% 1.13/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(657,plain,
% 1.13/1.38 (((~b(s(elem!1), z)) | (~b(s(z), 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), s(elem!1))) | (~b(s(z), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(658,plain,
% 1.13/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), 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(X0, 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), s(elem!1))) | (~b(s(z), z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[657])).
% 1.13/1.38 tff(659,plain,
% 1.13/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), 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(X0, 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), s(elem!1))) | (~b(s(z), z)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[658, 656])).
% 1.13/1.38 tff(660,plain,
% 1.13/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(661,plain,
% 1.13/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.13/1.38 tff(662,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[661, 245, 355, 655, 654, 645])).
% 1.13/1.38 tff(663,plain,((~r(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(664,plain,
% 1.13/1.38 (~b(s(z), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[663, 626, 289, 572])).
% 1.13/1.38 tff(665,plain,
% 1.13/1.38 (r(s(z), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[232, 664])).
% 1.13/1.38 tff(666,plain,
% 1.13/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(667,plain,
% 1.13/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(668,plain,
% 1.13/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.13/1.38 tff(669,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[668, 141, 289, 665, 619])).
% 1.13/1.38 tff(670,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(671,plain,
% 1.13/1.38 (~r(s(z), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[670, 571, 289, 9])).
% 1.13/1.38 tff(672,plain,
% 1.13/1.38 (b(s(z), elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[389, 671, 342])).
% 1.13/1.38 tff(673,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 1.13/1.38 tff(674,plain,
% 1.13/1.38 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[608, 614])).
% 1.13/1.38 tff(675,plain,
% 1.13/1.38 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[674])).
% 1.13/1.38 tff(676,plain,
% 1.13/1.38 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[675])).
% 1.13/1.38 tff(677,assumption,(elem!1 = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.38 tff(678,plain,
% 1.13/1.38 (s(s(s(s(s(z))))) = elem!1),
% 1.13/1.38 inference(symmetry,[status(thm)],[677])).
% 1.13/1.38 tff(679,plain,
% 1.13/1.38 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[678, 580])).
% 1.13/1.38 tff(680,plain,
% 1.13/1.38 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[679])).
% 1.13/1.38 tff(681,plain,
% 1.13/1.38 (s(s(s(s(z)))) = s(elem!1)),
% 1.13/1.38 inference(transitivity,[status(thm)],[604, 680, 113, 553])).
% 1.13/1.38 tff(682,plain,
% 1.13/1.38 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[681])).
% 1.13/1.38 tff(683,plain,
% 1.13/1.38 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[682])).
% 1.13/1.38 tff(684,plain,
% 1.13/1.38 (elem!1 = inj_0(s(elem!1))),
% 1.13/1.38 inference(symmetry,[status(thm)],[49])).
% 1.13/1.38 tff(685,plain,
% 1.13/1.38 (elem!1 = s(s(s(z)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[684, 683, 597])).
% 1.13/1.38 tff(686,plain,
% 1.13/1.38 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.13/1.38 inference(commutativity,[status(thm)],[])).
% 1.13/1.38 tff(687,plain,
% 1.13/1.38 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[678])).
% 1.13/1.38 tff(688,plain,
% 1.13/1.38 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(z))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[687, 686])).
% 1.13/1.38 tff(689,plain,
% 1.13/1.38 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[688])).
% 1.13/1.38 tff(690,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.38 tff(691,plain,
% 1.13/1.38 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[690])).
% 1.13/1.38 tff(692,plain,
% 1.13/1.38 (s(s(z)) = s(s(s(s(z))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[586, 691, 603])).
% 1.13/1.38 tff(693,plain,
% 1.13/1.38 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[692])).
% 1.13/1.38 tff(694,plain,
% 1.13/1.38 (s(z) = s(s(s(s(s(z)))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[591, 693, 597, 690])).
% 1.13/1.38 tff(695,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.38 tff(696,plain,
% 1.13/1.38 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[695])).
% 1.13/1.38 tff(697,plain,
% 1.13/1.38 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.13/1.38 inference(symmetry,[status(thm)],[696])).
% 1.13/1.38 tff(698,plain,
% 1.13/1.38 (s(s(s(s(z)))) = z),
% 1.13/1.38 inference(transitivity,[status(thm)],[604, 697, 52])).
% 1.13/1.38 tff(699,plain,
% 1.13/1.38 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(700,plain,
% 1.13/1.38 (~(s(s(s(s(z)))) = z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[699, 20])).
% 1.13/1.38 tff(701,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[700, 698])).
% 1.13/1.38 tff(702,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(703,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[702, 694])).
% 1.13/1.38 tff(704,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(705,plain,
% 1.13/1.38 (~(elem!1 = s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[704, 689])).
% 1.13/1.38 tff(706,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[705, 685])).
% 1.13/1.38 tff(707,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(708,plain,
% 1.13/1.38 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[707, 553, 199])).
% 1.13/1.38 tff(709,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.13/1.38 tff(710,plain,
% 1.13/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(711,plain,
% 1.13/1.38 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(712,plain,
% 1.13/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[711])).
% 1.13/1.38 tff(713,plain,
% 1.13/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[712, 710])).
% 1.13/1.38 tff(714,plain,
% 1.13/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(715,plain,
% 1.13/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[714, 713])).
% 1.13/1.38 tff(716,plain,
% 1.13/1.38 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[715, 245, 301, 447, 709])).
% 1.13/1.38 tff(717,plain,
% 1.13/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(718,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(719,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.13/1.38 tff(720,plain,
% 1.13/1.38 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[719, 32])).
% 1.13/1.38 tff(721,plain,
% 1.13/1.38 (r(elem!1, s(s(s(s(s(z))))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[720, 716, 708])).
% 1.13/1.38 tff(722,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.13/1.38 tff(723,assumption,(r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.13/1.38 tff(724,plain,
% 1.13/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(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(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(725,plain,
% 1.13/1.38 (((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(726,plain,
% 1.13/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[725])).
% 1.13/1.38 tff(727,plain,
% 1.13/1.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[726, 724])).
% 1.13/1.38 tff(728,plain,
% 1.13/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(729,plain,
% 1.13/1.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[728, 727])).
% 1.13/1.38 tff(730,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[729, 141, 131, 723, 722])).
% 1.13/1.38 tff(731,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(732,plain,
% 1.13/1.38 (~r(s(s(s(s(s(z))))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[731, 721, 131])).
% 1.13/1.38 tff(733,plain,
% 1.13/1.38 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(734,plain,
% 1.13/1.38 (~(s(s(s(s(s(z))))) = z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[733, 20])).
% 1.13/1.38 tff(735,plain,
% 1.13/1.38 (((~![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))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(736,plain,
% 1.13/1.38 ((~![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))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(737,plain,
% 1.13/1.38 ((~![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)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[736, 735])).
% 1.13/1.38 tff(738,plain,
% 1.13/1.38 (b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[737, 32, 734])).
% 1.13/1.38 tff(739,plain,
% 1.13/1.38 (b(s(s(s(s(s(z))))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[738, 732])).
% 1.13/1.38 tff(740,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.13/1.38 tff(741,plain,
% 1.13/1.38 (((~![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(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, elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(742,plain,
% 1.13/1.39 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(743,plain,
% 1.13/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[742])).
% 1.13/1.39 tff(744,plain,
% 1.13/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[743, 741])).
% 1.13/1.39 tff(745,plain,
% 1.13/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(746,plain,
% 1.13/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.13/1.39 tff(747,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[746, 141, 289, 723, 740])).
% 1.13/1.39 tff(748,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(749,plain,
% 1.13/1.39 (~r(z, s(s(s(s(s(z))))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[748, 721, 289])).
% 1.13/1.39 tff(750,plain,
% 1.13/1.39 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.13/1.39 inference(commutativity,[status(thm)],[])).
% 1.13/1.39 tff(751,plain,
% 1.13/1.39 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 1.13/1.39 inference(symmetry,[status(thm)],[750])).
% 1.13/1.39 tff(752,plain,
% 1.13/1.39 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[751])).
% 1.13/1.39 tff(753,plain,
% 1.13/1.39 (~(z = s(s(s(s(s(z))))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[734, 752])).
% 1.13/1.39 tff(754,plain,
% 1.13/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(755,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(756,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.13/1.39 tff(757,plain,
% 1.13/1.39 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[756, 32])).
% 1.13/1.39 tff(758,plain,
% 1.13/1.39 (b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[757, 753])).
% 1.13/1.39 tff(759,plain,
% 1.13/1.39 (b(z, s(s(s(s(s(z))))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[758, 749])).
% 1.13/1.39 tff(760,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(761,plain,
% 1.13/1.39 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(762,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[761])).
% 1.13/1.39 tff(763,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[762, 760])).
% 1.13/1.39 tff(764,plain,
% 1.13/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(765,plain,
% 1.13/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[764, 763])).
% 1.13/1.39 tff(766,plain,
% 1.13/1.39 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[765, 245, 288, 759, 709, 739])).
% 1.13/1.39 tff(767,plain,
% 1.13/1.39 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[766, 676])).
% 1.13/1.39 tff(768,plain,
% 1.13/1.39 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[674])).
% 1.13/1.39 tff(769,plain,
% 1.13/1.39 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[768])).
% 1.13/1.39 tff(770,plain,
% 1.13/1.39 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.13/1.39 inference(commutativity,[status(thm)],[])).
% 1.13/1.39 tff(771,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 1.13/1.39 tff(772,plain,
% 1.13/1.39 (elem!1 = s(s(s(s(s(z)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[771, 770])).
% 1.13/1.39 tff(773,assumption,(~(elem!1 = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.13/1.39 tff(774,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[773, 772])).
% 1.13/1.39 tff(775,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (elem!1 = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(776,plain,
% 1.13/1.39 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[775, 708])).
% 1.13/1.39 tff(777,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(778,plain,
% 1.13/1.39 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(779,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[778])).
% 1.13/1.39 tff(780,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.13/1.39 inference(transitivity,[status(thm)],[779, 777])).
% 1.13/1.39 tff(781,plain,
% 1.13/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(782,plain,
% 1.13/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.13/1.39 tff(783,plain,
% 1.13/1.39 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[782, 245, 301, 447, 709])).
% 1.13/1.39 tff(784,plain,
% 1.13/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(785,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(786,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.13/1.39 tff(787,plain,
% 1.13/1.39 ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[786, 32])).
% 1.13/1.39 tff(788,plain,
% 1.13/1.39 (r(s(s(s(s(s(z))))), elem!1)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[787, 783, 776])).
% 1.13/1.39 tff(789,plain,
% 1.13/1.39 (((~![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(z))))), elem!1)) | (~r(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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(790,plain,
% 1.13/1.39 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(791,plain,
% 1.13/1.39 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.13/1.39 tff(792,plain,
% 1.13/1.39 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[791, 141, 572, 788])).
% 1.13/1.39 tff(793,plain,
% 1.13/1.39 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[792, 769])).
% 1.13/1.39 tff(794,plain,
% 1.13/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(795,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(796,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[795, 794])).
% 1.13/1.39 tff(797,plain,
% 1.13/1.39 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[796, 32])).
% 1.13/1.39 tff(798,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[797, 793, 767, 673])).
% 1.13/1.39 tff(799,plain,((~b(s(s(s(s(s(z))))), s(z))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(800,plain,
% 1.13/1.39 (~b(s(s(s(s(s(z))))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[799, 672, 579, 199, 571, 288, 131, 289, 301, 613])).
% 1.13/1.39 tff(801,plain,
% 1.13/1.39 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.13/1.39 inference(commutativity,[status(thm)],[])).
% 1.13/1.39 tff(802,plain,
% 1.13/1.39 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.13/1.39 inference(symmetry,[status(thm)],[801])).
% 1.13/1.39 tff(803,plain,
% 1.13/1.39 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(z)))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[802])).
% 1.13/1.39 tff(804,plain,
% 1.13/1.39 (~(s(s(s(s(s(z))))) = s(z))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[702, 803])).
% 1.13/1.39 tff(805,plain,
% 1.13/1.39 (((~![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)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(806,plain,
% 1.13/1.39 ((~![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)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(807,plain,
% 1.13/1.39 ((~![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))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[806, 805])).
% 1.13/1.39 tff(808,plain,
% 1.13/1.39 ((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))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[807, 32])).
% 1.13/1.39 tff(809,plain,
% 1.13/1.39 (b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[808, 804])).
% 1.13/1.39 tff(810,plain,
% 1.13/1.39 (r(s(s(s(s(s(z))))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[809, 800])).
% 1.13/1.39 tff(811,plain,
% 1.13/1.39 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[579])).
% 1.13/1.39 tff(812,plain,
% 1.13/1.39 (b(z, s(elem!1))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[293, 811])).
% 1.13/1.39 tff(813,plain,
% 1.13/1.39 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[579])).
% 1.13/1.39 tff(814,plain,
% 1.13/1.39 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.13/1.39 inference(transitivity,[status(thm)],[312, 255, 813, 49])).
% 1.13/1.39 tff(815,plain,
% 1.13/1.39 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), elem!1)),
% 1.13/1.39 inference(monotonicity,[status(thm)],[814])).
% 1.13/1.39 tff(816,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.13/1.39 tff(817,plain,
% 1.13/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(818,plain,
% 1.13/1.39 (((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(819,plain,
% 1.13/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[818])).
% 1.13/1.39 tff(820,plain,
% 1.13/1.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[819, 817])).
% 1.13/1.39 tff(821,plain,
% 1.13/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(822,plain,
% 1.13/1.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.13/1.39 tff(823,plain,
% 1.13/1.39 (~r(s(elem!1), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[822, 141, 572, 816])).
% 1.13/1.39 tff(824,plain,
% 1.13/1.39 (((~![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)))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(825,plain,
% 1.13/1.39 ((~![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)))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(826,plain,
% 1.13/1.39 ((~![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))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[825, 824])).
% 1.13/1.39 tff(827,plain,
% 1.13/1.39 (b(s(elem!1), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[826, 32, 610, 823])).
% 1.13/1.39 tff(828,plain,
% 1.13/1.39 (((~![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)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(829,plain,
% 1.13/1.39 ((~![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)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(830,plain,
% 1.13/1.39 ((~![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))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.13/1.39 tff(831,plain,
% 1.13/1.39 (~r(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[830, 141, 289, 816])).
% 1.13/1.39 tff(832,plain,
% 1.13/1.39 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(833,plain,
% 1.13/1.39 (~(s(s(s(z))) = z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[832, 20])).
% 1.13/1.39 tff(834,plain,
% 1.13/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(835,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(836,plain,
% 1.13/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[835, 834])).
% 1.13/1.39 tff(837,plain,
% 1.13/1.39 (b(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[836, 32, 833, 831])).
% 1.13/1.39 tff(838,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.13/1.39 tff(839,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(840,plain,
% 1.13/1.39 (((~b(s(elem!1), z)) | (~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(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(841,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(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(X0, 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), s(s(s(z)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[840])).
% 1.13/1.39 tff(842,plain,
% 1.13/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(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(X0, 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), s(s(s(z))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[841, 839])).
% 1.13/1.39 tff(843,plain,
% 1.13/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(844,plain,
% 1.13/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.13/1.40 inference(modus_ponens,[status(thm)],[843, 842])).
% 1.13/1.40 tff(845,plain,
% 1.13/1.40 ($false),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[844, 245, 288, 838, 837, 827])).
% 1.13/1.40 tff(846,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.40 tff(847,plain,
% 1.13/1.40 (~r(s(s(s(z))), elem!1)),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[846, 812, 289, 571, 595, 288])).
% 1.13/1.40 tff(848,plain,
% 1.13/1.40 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.13/1.40 inference(monotonicity,[status(thm)],[553])).
% 1.13/1.40 tff(849,plain,
% 1.13/1.40 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.13/1.40 inference(transitivity,[status(thm)],[312, 255, 848, 49])).
% 1.13/1.40 tff(850,plain,
% 1.13/1.40 (r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(z))), elem!1)),
% 1.13/1.40 inference(monotonicity,[status(thm)],[849])).
% 1.13/1.40 tff(851,assumption,(r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.13/1.40 tff(852,plain,
% 1.13/1.40 (r(s(s(s(z))), elem!1)),
% 1.13/1.40 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.13/1.40 tff(853,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.13/1.40 tff(854,plain,
% 1.13/1.40 ($false),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[853, 852])).
% 1.13/1.40 tff(855,plain,((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(z))), elem!1) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.40 tff(856,plain,
% 1.13/1.40 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[855, 847, 579, 199])).
% 1.13/1.40 tff(857,plain,
% 1.13/1.40 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = elem!1)),
% 1.13/1.40 inference(monotonicity,[status(thm)],[814])).
% 1.13/1.40 tff(858,plain,
% 1.13/1.40 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(z))))),
% 1.13/1.40 inference(transitivity,[status(thm)],[857, 686])).
% 1.13/1.40 tff(859,plain,
% 1.13/1.40 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.40 inference(symmetry,[status(thm)],[858])).
% 1.13/1.40 tff(860,plain,
% 1.13/1.40 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.40 inference(transitivity,[status(thm)],[686, 859])).
% 1.13/1.40 tff(861,plain,
% 1.13/1.40 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.40 inference(monotonicity,[status(thm)],[860])).
% 1.13/1.40 tff(862,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.13/1.40 tff(863,plain,
% 1.13/1.40 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.13/1.40 inference(transitivity,[status(thm)],[862, 580])).
% 1.13/1.40 tff(864,plain,
% 1.13/1.40 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.40 inference(monotonicity,[status(thm)],[863])).
% 1.13/1.40 tff(865,plain,
% 1.13/1.40 (s(s(z)) = s(elem!1)),
% 1.13/1.40 inference(transitivity,[status(thm)],[586, 864, 113, 553])).
% 1.13/1.40 tff(866,plain,
% 1.13/1.40 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.13/1.40 inference(monotonicity,[status(thm)],[865])).
% 1.13/1.40 tff(867,plain,
% 1.13/1.40 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.13/1.40 inference(symmetry,[status(thm)],[866])).
% 1.13/1.40 tff(868,plain,
% 1.13/1.40 (elem!1 = s(z)),
% 1.13/1.40 inference(transitivity,[status(thm)],[684, 867, 590])).
% 1.13/1.40 tff(869,plain,
% 1.13/1.40 ($false),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[210, 868])).
% 1.13/1.40 tff(870,plain,((~(s(s(s(z))) = elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.40 tff(871,plain,
% 1.13/1.40 (~(s(s(s(z))) = elem!1)),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[870, 579, 199])).
% 1.13/1.40 tff(872,plain,
% 1.13/1.40 (~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.13/1.40 inference(modus_ponens,[status(thm)],[871, 861])).
% 1.13/1.40 tff(873,plain,
% 1.13/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.40 inference(rewrite,[status(thm)],[])).
% 1.13/1.40 tff(874,plain,
% 1.13/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.13/1.40 inference(quant_inst,[status(thm)],[])).
% 1.13/1.40 tff(875,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[874, 873])).
% 1.23/1.40 tff(876,plain,
% 1.23/1.40 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[875, 32])).
% 1.23/1.40 tff(877,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[876, 872, 856])).
% 1.23/1.40 tff(878,plain,
% 1.23/1.40 (b(s(s(s(z))), elem!1)),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[877, 815])).
% 1.23/1.40 tff(879,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(880,plain,
% 1.23/1.40 (((~b(s(z), elem!1)) | (~b(s(s(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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(881,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(z))), elem!1))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[880])).
% 1.23/1.40 tff(882,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(z))), elem!1)))),
% 1.23/1.40 inference(transitivity,[status(thm)],[881, 879])).
% 1.23/1.40 tff(883,plain,
% 1.23/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(884,plain,
% 1.23/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.23/1.40 tff(885,plain,
% 1.23/1.40 (~b(s(s(s(z))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[884, 245, 301, 672, 878])).
% 1.23/1.40 tff(886,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.23/1.40 tff(887,plain,
% 1.23/1.40 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[886])).
% 1.23/1.40 tff(888,plain,
% 1.23/1.40 (s(s(z)) = z),
% 1.23/1.40 inference(transitivity,[status(thm)],[586, 887, 52])).
% 1.23/1.40 tff(889,plain,
% 1.23/1.40 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(890,plain,
% 1.23/1.40 (~(s(s(z)) = z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[889, 20])).
% 1.23/1.40 tff(891,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[890, 888])).
% 1.23/1.40 tff(892,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(893,plain,
% 1.23/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(894,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(895,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[894, 893])).
% 1.23/1.40 tff(896,plain,
% 1.23/1.40 (r(s(s(s(z))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[895, 32, 892, 885])).
% 1.23/1.40 tff(897,plain,
% 1.23/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(898,plain,
% 1.23/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(899,plain,
% 1.23/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.23/1.40 tff(900,plain,
% 1.23/1.40 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[899, 141, 896, 810])).
% 1.23/1.40 tff(901,plain,
% 1.23/1.40 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.23/1.40 inference(commutativity,[status(thm)],[])).
% 1.23/1.40 tff(902,plain,
% 1.23/1.40 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.23/1.40 inference(symmetry,[status(thm)],[901])).
% 1.23/1.40 tff(903,plain,
% 1.23/1.40 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[902])).
% 1.23/1.40 tff(904,plain,
% 1.23/1.40 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[704, 903])).
% 1.23/1.40 tff(905,plain,
% 1.23/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(906,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(907,plain,
% 1.23/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.23/1.40 tff(908,plain,
% 1.23/1.40 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[907, 32])).
% 1.23/1.40 tff(909,plain,
% 1.23/1.40 (b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[908, 904])).
% 1.23/1.40 tff(910,plain,
% 1.23/1.40 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[909, 900])).
% 1.23/1.40 tff(911,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.23/1.40 tff(912,plain,
% 1.23/1.40 (~b(s(elem!1), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[844, 245, 288, 838, 911])).
% 1.23/1.40 tff(913,plain,
% 1.23/1.40 (r(s(elem!1), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[826, 32, 610, 912])).
% 1.23/1.40 tff(914,plain,
% 1.23/1.40 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[686])).
% 1.23/1.40 tff(915,plain,
% 1.23/1.40 (~(s(s(s(z))) = elem!1)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[870, 553, 199])).
% 1.23/1.40 tff(916,plain,
% 1.23/1.40 (~(elem!1 = s(s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.23/1.40 tff(917,plain,
% 1.23/1.40 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[612, 553, 199, 610])).
% 1.23/1.40 tff(918,plain,
% 1.23/1.40 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.40 inference(symmetry,[status(thm)],[768])).
% 1.23/1.40 tff(919,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.23/1.40 tff(920,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(921,plain,
% 1.23/1.40 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(922,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[921])).
% 1.23/1.40 tff(923,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[922, 920])).
% 1.23/1.40 tff(924,plain,
% 1.23/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(925,plain,
% 1.23/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[924, 923])).
% 1.23/1.40 tff(926,plain,
% 1.23/1.40 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[925, 245, 288, 838, 919])).
% 1.23/1.40 tff(927,plain,
% 1.23/1.40 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[926, 676])).
% 1.23/1.40 tff(928,plain,
% 1.23/1.40 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[797, 927, 673])).
% 1.23/1.40 tff(929,plain,
% 1.23/1.40 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[928, 918])).
% 1.23/1.40 tff(930,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.23/1.40 tff(931,assumption,(~(s(s(s(s(s(z))))) = s(s(s(z))))), introduced(assumption)).
% 1.23/1.40 tff(932,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), 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(X0, 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(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(933,plain,
% 1.23/1.40 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(934,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), 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(X0, 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(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[933])).
% 1.23/1.40 tff(935,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), 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(X0, 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(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[934, 932])).
% 1.23/1.40 tff(936,plain,
% 1.23/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(937,plain,
% 1.23/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[936, 935])).
% 1.23/1.40 tff(938,plain,
% 1.23/1.40 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[937, 245, 288, 838, 911, 919])).
% 1.23/1.40 tff(939,plain,
% 1.23/1.40 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[908, 938, 931])).
% 1.23/1.40 tff(940,plain,
% 1.23/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(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(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(941,plain,
% 1.23/1.40 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(942,plain,
% 1.23/1.40 (((~![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(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[941])).
% 1.23/1.40 tff(943,plain,
% 1.23/1.40 (((~![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(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[942, 940])).
% 1.23/1.40 tff(944,plain,
% 1.23/1.40 ((~![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(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(945,plain,
% 1.23/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[944, 943])).
% 1.23/1.40 tff(946,plain,
% 1.23/1.40 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[945, 141, 939, 930])).
% 1.23/1.40 tff(947,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[946, 929])).
% 1.23/1.40 tff(948,plain,((~b(s(s(s(s(s(z))))), z)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(z))))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(949,plain,
% 1.23/1.40 ((~b(s(s(s(s(s(z))))), z)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[948, 904])).
% 1.23/1.40 tff(950,plain,
% 1.23/1.40 (~b(s(s(s(s(s(z))))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[949, 913, 199, 917, 911, 288, 838, 553])).
% 1.23/1.40 tff(951,plain,
% 1.23/1.40 (r(s(s(s(s(s(z))))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[738, 950])).
% 1.23/1.40 tff(952,plain,
% 1.23/1.40 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[731, 951, 131])).
% 1.23/1.40 tff(953,plain,
% 1.23/1.40 (b(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[720, 952, 708])).
% 1.23/1.40 tff(954,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.23/1.40 tff(955,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.40 tff(956,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(957,plain,
% 1.23/1.40 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(958,plain,
% 1.23/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[957])).
% 1.23/1.41 tff(959,plain,
% 1.23/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[958, 956])).
% 1.23/1.41 tff(960,plain,
% 1.23/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(961,plain,
% 1.23/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[960, 959])).
% 1.23/1.41 tff(962,plain,
% 1.23/1.41 ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[961, 245, 301, 955, 954])).
% 1.23/1.41 tff(963,plain,
% 1.23/1.41 (~b(elem!1, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[962, 953])).
% 1.23/1.41 tff(964,plain,
% 1.23/1.41 (((~![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)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(965,plain,
% 1.23/1.41 ((~![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)))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(966,plain,
% 1.23/1.41 ((~![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))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[965, 964])).
% 1.23/1.41 tff(967,plain,
% 1.23/1.41 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[966, 32])).
% 1.23/1.41 tff(968,plain,
% 1.23/1.41 (r(elem!1, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[967, 963, 916])).
% 1.23/1.41 tff(969,plain,
% 1.23/1.41 (((~![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(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(970,plain,
% 1.23/1.41 (((~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(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(971,plain,
% 1.23/1.41 (((~![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(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[970])).
% 1.23/1.41 tff(972,plain,
% 1.23/1.41 (((~![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(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[971, 969])).
% 1.23/1.41 tff(973,plain,
% 1.23/1.41 ((~![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)))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(974,plain,
% 1.23/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[973, 972])).
% 1.23/1.41 tff(975,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[974, 141, 572, 968, 913])).
% 1.23/1.41 tff(976,plain,((~b(s(s(s(z))), z)) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(977,plain,
% 1.23/1.41 (~b(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[976, 571, 301, 910, 878, 131, 199, 288, 812, 579, 595])).
% 1.23/1.41 tff(978,plain,
% 1.23/1.41 (r(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[836, 32, 833, 977])).
% 1.23/1.41 tff(979,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.23/1.41 tff(980,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.23/1.41 tff(981,plain,
% 1.23/1.41 (((~![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))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(982,plain,
% 1.23/1.41 ((~![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))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(983,plain,
% 1.23/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[982, 981])).
% 1.23/1.41 tff(984,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[983, 141, 220, 980, 979])).
% 1.23/1.41 tff(985,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(986,plain,
% 1.23/1.41 (~r(s(z), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[985, 978, 896])).
% 1.23/1.41 tff(987,plain,
% 1.23/1.41 (b(s(z), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[232, 986])).
% 1.23/1.41 tff(988,plain,
% 1.23/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(989,plain,
% 1.23/1.41 (((~b(s(elem!1), z)) | (~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))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(990,plain,
% 1.23/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(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(X0, 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)))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[989])).
% 1.23/1.41 tff(991,plain,
% 1.23/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(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(X0, 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))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[990, 988])).
% 1.23/1.41 tff(992,plain,
% 1.23/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(993,plain,
% 1.23/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.23/1.41 tff(994,plain,
% 1.23/1.41 (~b(s(elem!1), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[993, 245, 987, 288, 812])).
% 1.23/1.41 tff(995,plain,
% 1.23/1.41 (r(s(elem!1), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[369, 994, 348])).
% 1.23/1.41 tff(996,assumption,(r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.23/1.41 tff(997,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.23/1.41 tff(998,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.23/1.41 tff(999,plain,
% 1.23/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1000,plain,
% 1.23/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1001,plain,
% 1.23/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1000, 999])).
% 1.23/1.41 tff(1002,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1001, 141, 998, 997, 996])).
% 1.23/1.41 tff(1003,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1004,plain,
% 1.23/1.41 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1003, 995, 810])).
% 1.23/1.41 tff(1005,plain,
% 1.23/1.41 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1004, 618])).
% 1.23/1.41 tff(1006,plain,
% 1.23/1.41 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[616])).
% 1.23/1.41 tff(1007,plain,
% 1.23/1.41 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1006])).
% 1.23/1.41 tff(1008,plain,
% 1.23/1.41 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[707, 579, 199])).
% 1.23/1.41 tff(1009,plain,
% 1.23/1.41 (~(elem!1 = s(s(s(z))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[871, 914])).
% 1.23/1.41 tff(1010,plain,
% 1.23/1.41 (((~![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))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1011,plain,
% 1.23/1.41 (((~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))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1012,plain,
% 1.23/1.41 (((~![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)))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1011])).
% 1.23/1.41 tff(1013,plain,
% 1.23/1.41 (((~![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))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1012, 1010])).
% 1.23/1.41 tff(1014,plain,
% 1.23/1.41 ((~![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))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1015,plain,
% 1.23/1.41 ((~![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)))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 1.23/1.41 tff(1016,plain,
% 1.23/1.41 (~r(elem!1, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1015, 141, 131, 978])).
% 1.23/1.41 tff(1017,plain,
% 1.23/1.41 (b(elem!1, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[967, 1016, 1009])).
% 1.23/1.41 tff(1018,plain,
% 1.23/1.41 ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[961, 245, 301, 910, 878])).
% 1.23/1.41 tff(1019,plain,
% 1.23/1.41 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1018, 1017])).
% 1.23/1.41 tff(1020,plain,
% 1.23/1.41 (r(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[720, 1019, 1008])).
% 1.23/1.41 tff(1021,plain,
% 1.23/1.41 (~r(s(s(s(s(s(z))))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[731, 1020, 131])).
% 1.23/1.41 tff(1022,plain,
% 1.23/1.41 (b(s(s(s(s(s(z))))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[738, 1021])).
% 1.23/1.41 tff(1023,plain,
% 1.23/1.41 (~r(z, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[748, 1020, 289])).
% 1.23/1.41 tff(1024,plain,
% 1.23/1.41 (b(z, s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[758, 1023])).
% 1.23/1.41 tff(1025,plain,
% 1.23/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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(z))))), s(elem!1))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1026,plain,
% 1.23/1.41 (((~b(s(s(s(s(s(z))))), 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(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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(z))))), s(elem!1))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1027,plain,
% 1.23/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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(z))))), s(elem!1)))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1026])).
% 1.23/1.41 tff(1028,plain,
% 1.23/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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(z))))), s(elem!1))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1027, 1025])).
% 1.23/1.41 tff(1029,plain,
% 1.23/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1030,plain,
% 1.23/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 1.23/1.41 tff(1031,plain,
% 1.23/1.41 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1030, 245, 288, 910, 1024, 1022])).
% 1.23/1.41 tff(1032,plain,
% 1.23/1.41 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1031, 1007])).
% 1.23/1.41 tff(1033,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[797, 1032, 1005, 613])).
% 1.23/1.41 tff(1034,plain,((~b(s(elem!1), z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = elem!1) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1035,plain,
% 1.23/1.41 (~b(s(elem!1), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1034, 152, 129, 176, 287, 9, 170, 169, 168, 164])).
% 1.23/1.41 tff(1036,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.23/1.41 tff(1037,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.23/1.41 tff(1038,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[653, 32, 638, 1037, 1036])).
% 1.23/1.41 tff(1039,plain,(b(s(elem!1), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1040,plain,
% 1.23/1.41 (r(s(elem!1), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1039, 1035])).
% 1.23/1.41 tff(1041,plain,
% 1.23/1.41 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.23/1.41 inference(transitivity,[status(thm)],[604, 680, 113])).
% 1.23/1.41 tff(1042,plain,
% 1.23/1.41 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1041])).
% 1.23/1.41 tff(1043,plain,
% 1.23/1.41 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.23/1.41 inference(symmetry,[status(thm)],[597])).
% 1.23/1.41 tff(1044,plain,
% 1.23/1.41 (s(s(s(z))) = s(s(elem!1))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1043, 1042, 157])).
% 1.23/1.41 tff(1045,plain,
% 1.23/1.41 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1044])).
% 1.23/1.41 tff(1046,plain,
% 1.23/1.41 (s(s(z)) = s(elem!1)),
% 1.23/1.41 inference(transitivity,[status(thm)],[586, 1045, 155])).
% 1.23/1.41 tff(1047,plain,
% 1.23/1.41 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1046])).
% 1.23/1.41 tff(1048,plain,
% 1.23/1.41 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.23/1.41 inference(symmetry,[status(thm)],[1047])).
% 1.23/1.41 tff(1049,plain,
% 1.23/1.41 (elem!1 = s(z)),
% 1.23/1.41 inference(transitivity,[status(thm)],[684, 1048, 590])).
% 1.23/1.41 tff(1050,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[210, 1049])).
% 1.23/1.41 tff(1051,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1052,plain,
% 1.23/1.41 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1051, 152])).
% 1.23/1.41 tff(1053,plain,
% 1.23/1.41 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[775, 1052])).
% 1.23/1.41 tff(1054,assumption,(s(elem!1) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.41 tff(1055,plain,
% 1.23/1.41 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.23/1.41 inference(symmetry,[status(thm)],[1054])).
% 1.23/1.41 tff(1056,plain,
% 1.23/1.41 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1055])).
% 1.23/1.41 tff(1057,plain,
% 1.23/1.41 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[604, 1056, 49, 580])).
% 1.23/1.41 tff(1058,plain,
% 1.23/1.41 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1057])).
% 1.23/1.41 tff(1059,plain,
% 1.23/1.41 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1043, 1058, 113])).
% 1.23/1.41 tff(1060,plain,
% 1.23/1.41 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1059])).
% 1.23/1.41 tff(1061,plain,
% 1.23/1.41 (s(s(z)) = s(s(elem!1))),
% 1.23/1.41 inference(transitivity,[status(thm)],[586, 1060, 157])).
% 1.23/1.41 tff(1062,plain,
% 1.23/1.41 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1061])).
% 1.23/1.41 tff(1063,plain,
% 1.23/1.41 (s(z) = s(elem!1)),
% 1.23/1.41 inference(transitivity,[status(thm)],[591, 1062, 155])).
% 1.23/1.41 tff(1064,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[9, 1063])).
% 1.23/1.41 tff(1065,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (s(z) = s(elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1066,plain,
% 1.23/1.41 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1065, 9, 152])).
% 1.23/1.41 tff(1067,plain,
% 1.23/1.41 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[152])).
% 1.23/1.41 tff(1068,plain,
% 1.23/1.41 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.23/1.41 inference(transitivity,[status(thm)],[1067, 339])).
% 1.23/1.41 tff(1069,plain,
% 1.23/1.41 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1068])).
% 1.23/1.41 tff(1070,plain,
% 1.23/1.41 (~(s(z) = elem!1)),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[209, 1069])).
% 1.23/1.41 tff(1071,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.23/1.41 tff(1072,plain,
% 1.23/1.41 (s(elem!1) = elem!1),
% 1.23/1.41 inference(symmetry,[status(thm)],[1071])).
% 1.23/1.41 tff(1073,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[169, 1072])).
% 1.23/1.41 tff(1074,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(1075,plain,
% 1.23/1.41 (~(elem!1 = s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1074, 169])).
% 1.23/1.41 tff(1076,plain,
% 1.23/1.41 (((~![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)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1077,plain,
% 1.23/1.41 (((~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)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(1078,plain,
% 1.23/1.41 (((~![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))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[1077])).
% 1.23/1.41 tff(1079,plain,
% 1.23/1.41 (((~![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)))),
% 1.23/1.41 inference(transitivity,[status(thm)],[1078, 1076])).
% 1.23/1.41 tff(1080,plain,
% 1.23/1.41 ((~![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))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(1081,plain,
% 1.23/1.41 ((~![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))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 1.23/1.41 tff(1082,plain,
% 1.23/1.41 ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1081, 141])).
% 1.23/1.41 tff(1083,plain,
% 1.23/1.41 (~r(elem!1, s(elem!1))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1082, 1040, 129])).
% 1.23/1.42 tff(1084,plain,
% 1.23/1.42 (((~![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)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1085,plain,
% 1.23/1.42 ((~![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)))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1086,plain,
% 1.23/1.42 ((~![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))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 1.23/1.42 tff(1087,plain,
% 1.23/1.42 (b(elem!1, s(elem!1))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1086, 32, 1083, 1075])).
% 1.23/1.42 tff(1088,plain,
% 1.23/1.42 (~r(s(elem!1), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[649, 1040, 176])).
% 1.23/1.42 tff(1089,plain,
% 1.23/1.42 (b(s(elem!1), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[570, 1088, 169])).
% 1.23/1.42 tff(1090,plain,
% 1.23/1.42 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[152])).
% 1.23/1.42 tff(1091,plain,
% 1.23/1.42 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.42 inference(symmetry,[status(thm)],[1090])).
% 1.23/1.42 tff(1092,plain,
% 1.23/1.42 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1091])).
% 1.23/1.42 tff(1093,plain,
% 1.23/1.42 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1083, 1092])).
% 1.23/1.42 tff(1094,plain,
% 1.23/1.42 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[420, 1093, 164])).
% 1.23/1.42 tff(1095,plain,
% 1.23/1.42 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[223, 141, 220, 106])).
% 1.23/1.42 tff(1096,plain,
% 1.23/1.42 (b(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[217, 1095])).
% 1.23/1.42 tff(1097,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.23/1.42 tff(1098,plain,
% 1.23/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1099,plain,
% 1.23/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1100,plain,
% 1.23/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 1.23/1.42 tff(1101,plain,
% 1.23/1.42 (~r(s(z), s(elem!1))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1100, 141, 1097, 220])).
% 1.23/1.42 tff(1102,plain,
% 1.23/1.42 (b(s(z), s(elem!1))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[440, 1101, 9])).
% 1.23/1.42 tff(1103,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.23/1.42 tff(1104,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1105,plain,
% 1.23/1.42 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1106,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1105])).
% 1.23/1.42 tff(1107,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1106, 1104])).
% 1.23/1.42 tff(1108,plain,
% 1.23/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1109,plain,
% 1.23/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.23/1.42 tff(1110,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1109, 245, 308, 1103, 1102, 10, 1096])).
% 1.23/1.42 tff(1111,plain,((~r(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1112,plain,
% 1.23/1.42 (~r(s(z), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1111, 1094, 106, 1040, 9, 1089, 1087])).
% 1.23/1.42 tff(1113,plain,
% 1.23/1.42 (b(s(z), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[232, 1112])).
% 1.23/1.42 tff(1114,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1115,plain,
% 1.23/1.42 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), 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))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1116,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(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(X0, 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)))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1115])).
% 1.23/1.42 tff(1117,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(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(X0, 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))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1116, 1114])).
% 1.23/1.42 tff(1118,plain,
% 1.23/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1119,plain,
% 1.23/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.23/1.42 tff(1120,plain,
% 1.23/1.42 (~b(s(z), s(s(s(elem!1))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1119, 245, 198, 181, 1113])).
% 1.23/1.42 tff(1121,plain,
% 1.23/1.42 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.23/1.42 inference(commutativity,[status(thm)],[])).
% 1.23/1.42 tff(1122,plain,
% 1.23/1.42 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.23/1.42 inference(symmetry,[status(thm)],[1121])).
% 1.23/1.42 tff(1123,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.23/1.42 tff(1124,plain,
% 1.23/1.42 (s(s(s(elem!1))) = s(z)),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.23/1.42 tff(1125,assumption,(~(s(s(s(elem!1))) = s(z))), introduced(assumption)).
% 1.23/1.42 tff(1126,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1125, 1124])).
% 1.23/1.42 tff(1127,plain,((~(s(z) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1128,plain,
% 1.23/1.42 (~(s(z) = s(s(s(elem!1))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1127, 260])).
% 1.23/1.42 tff(1129,plain,
% 1.23/1.42 (((~![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)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1130,plain,
% 1.23/1.42 ((~![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)))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1131,plain,
% 1.23/1.42 ((~![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))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 1.23/1.42 tff(1132,plain,
% 1.23/1.42 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1131, 32])).
% 1.23/1.42 tff(1133,plain,
% 1.23/1.42 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1132, 1128])).
% 1.23/1.42 tff(1134,plain,
% 1.23/1.42 (r(s(z), s(s(s(elem!1))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1133, 1120])).
% 1.23/1.42 tff(1135,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.42 tff(1136,plain,
% 1.23/1.42 (((~![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), s(s(s(elem!1))))) | (~r(s(z), 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), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1137,plain,
% 1.23/1.42 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1138,plain,
% 1.23/1.42 (((~![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), s(s(s(elem!1))))) | (~r(s(z), elem!1))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1137])).
% 1.23/1.42 tff(1139,plain,
% 1.23/1.42 (((~![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), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1138, 1136])).
% 1.23/1.42 tff(1140,plain,
% 1.23/1.42 ((~![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))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1141,plain,
% 1.23/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 1.23/1.42 tff(1142,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1141, 141, 619, 170, 1135])).
% 1.23/1.42 tff(1143,plain,((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1144,plain,
% 1.23/1.42 (~r(s(z), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1143, 1134, 170])).
% 1.23/1.42 tff(1145,plain,
% 1.23/1.42 (b(s(z), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[389, 1144, 1070])).
% 1.23/1.42 tff(1146,plain,
% 1.23/1.42 (((~![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(s(z))))), z)) | (~r(s(elem!1), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1147,plain,
% 1.23/1.42 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1148,plain,
% 1.23/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1147])).
% 1.23/1.42 tff(1149,plain,
% 1.23/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1148, 1146])).
% 1.23/1.42 tff(1150,plain,
% 1.23/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1151,plain,
% 1.23/1.42 ((~![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(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.23/1.42 tff(1152,plain,
% 1.23/1.42 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1151, 141, 1097, 722])).
% 1.23/1.42 tff(1153,assumption,(~(s(elem!1) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.23/1.42 tff(1154,plain,
% 1.23/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), 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(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1155,plain,
% 1.23/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1156,plain,
% 1.23/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.23/1.42 tff(1157,plain,
% 1.23/1.42 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1156, 32, 1153, 1152])).
% 1.23/1.42 tff(1158,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.23/1.42 tff(1159,plain,
% 1.23/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1160,plain,
% 1.23/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1161,plain,
% 1.23/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.23/1.42 tff(1162,plain,
% 1.23/1.42 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1161, 141, 131, 722])).
% 1.23/1.42 tff(1163,plain,
% 1.23/1.42 (b(s(s(s(s(s(z))))), elem!1)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[787, 1162, 1158])).
% 1.23/1.42 tff(1164,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1165,plain,
% 1.23/1.42 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1166,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1165])).
% 1.23/1.42 tff(1167,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1166, 1164])).
% 1.23/1.42 tff(1168,plain,
% 1.23/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(1169,plain,
% 1.23/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 1.23/1.42 tff(1170,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1169, 245, 301, 308, 447, 1163, 1157])).
% 1.23/1.42 tff(1171,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(elem!1), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(1172,plain,
% 1.23/1.42 (~r(s(s(s(s(s(z))))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1171, 287, 1089, 1145, 1066, 1053, 1040, 129])).
% 1.23/1.42 tff(1173,plain,
% 1.23/1.42 (b(s(s(s(s(s(z))))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[738, 1172])).
% 1.23/1.42 tff(1174,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1175,plain,
% 1.23/1.42 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(1176,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[1175])).
% 1.23/1.42 tff(1177,plain,
% 1.23/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[1176, 1174])).
% 1.23/1.42 tff(1178,plain,
% 1.23/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1179,plain,
% 1.23/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 1.23/1.43 tff(1180,plain,
% 1.23/1.43 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1179, 245, 198, 181, 1173])).
% 1.23/1.43 tff(1181,plain,
% 1.23/1.43 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1180, 163])).
% 1.23/1.43 tff(1182,plain,
% 1.23/1.43 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[161])).
% 1.23/1.43 tff(1183,plain,
% 1.23/1.43 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1182])).
% 1.23/1.43 tff(1184,plain,
% 1.23/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1185,plain,
% 1.23/1.43 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1186,plain,
% 1.23/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1185])).
% 1.23/1.43 tff(1187,plain,
% 1.23/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1186, 1184])).
% 1.23/1.43 tff(1188,plain,
% 1.23/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1189,plain,
% 1.23/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 1.23/1.43 tff(1190,plain,
% 1.23/1.43 (~b(s(s(s(s(s(z))))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1189, 245, 198, 181, 1113, 1173])).
% 1.23/1.43 tff(1191,plain,
% 1.23/1.43 (r(s(s(s(s(s(z))))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[809, 1190])).
% 1.23/1.43 tff(1192,plain,
% 1.23/1.43 (~b(s(s(s(elem!1))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[251, 245, 198, 181, 1113])).
% 1.23/1.43 tff(1193,plain,
% 1.23/1.43 (r(s(s(s(elem!1))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[265, 1192])).
% 1.23/1.43 tff(1194,plain,
% 1.23/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1195,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1196,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.23/1.43 tff(1197,plain,
% 1.23/1.43 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1196, 141, 1193, 1191])).
% 1.23/1.43 tff(1198,plain,
% 1.23/1.43 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1197, 1183])).
% 1.23/1.43 tff(1199,plain,
% 1.23/1.43 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[797, 1198, 1181])).
% 1.23/1.43 tff(1200,plain,
% 1.23/1.43 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1199, 160])).
% 1.23/1.43 tff(1201,plain,
% 1.23/1.43 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1200])).
% 1.23/1.43 tff(1202,plain,
% 1.23/1.43 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.23/1.43 inference(transitivity,[status(thm)],[604, 1201, 157])).
% 1.23/1.43 tff(1203,plain,
% 1.23/1.43 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1202])).
% 1.23/1.43 tff(1204,plain,
% 1.23/1.43 (s(s(s(z))) = s(elem!1)),
% 1.23/1.43 inference(transitivity,[status(thm)],[1043, 1203, 155])).
% 1.23/1.43 tff(1205,plain,
% 1.23/1.43 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1204])).
% 1.23/1.43 tff(1206,plain,
% 1.23/1.43 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[586, 1205, 49, 153])).
% 1.23/1.43 tff(1207,plain,
% 1.23/1.43 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1206])).
% 1.23/1.43 tff(1208,plain,
% 1.23/1.43 (s(z) = s(s(s(elem!1)))),
% 1.23/1.43 inference(transitivity,[status(thm)],[591, 1207, 113])).
% 1.23/1.43 tff(1209,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1128, 1208])).
% 1.23/1.43 tff(1210,plain,((s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(elem!1) = elem!1) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(s(elem!1)))), elem!1) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1211,plain,
% 1.23/1.43 (s(z) = s(elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1210, 111, 106, 7, 105, 88, 8, 89, 90])).
% 1.23/1.43 tff(1212,plain,
% 1.23/1.43 (s(s(z)) = s(s(elem!1))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1211])).
% 1.23/1.43 tff(1213,plain,
% 1.23/1.43 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1212])).
% 1.23/1.43 tff(1214,plain,
% 1.23/1.43 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1213])).
% 1.23/1.43 tff(1215,plain,
% 1.23/1.43 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1214])).
% 1.23/1.43 tff(1216,plain,
% 1.23/1.43 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1215])).
% 1.23/1.43 tff(1217,plain,
% 1.23/1.43 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1218,plain,
% 1.23/1.43 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1))))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1217, 47])).
% 1.23/1.43 tff(1219,plain,
% 1.23/1.43 (z = elem!1),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[57, 1211])).
% 1.23/1.43 tff(1220,plain,
% 1.23/1.43 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1219])).
% 1.23/1.43 tff(1221,plain,
% 1.23/1.43 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[106, 1220])).
% 1.23/1.43 tff(1222,plain,
% 1.23/1.43 (s(elem!1) = s(z)),
% 1.23/1.43 inference(symmetry,[status(thm)],[1211])).
% 1.23/1.43 tff(1223,plain,
% 1.23/1.43 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1222])).
% 1.23/1.43 tff(1224,plain,
% 1.23/1.43 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1223, 1121])).
% 1.23/1.43 tff(1225,plain,
% 1.23/1.43 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1224])).
% 1.23/1.43 tff(1226,plain,
% 1.23/1.43 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1225])).
% 1.23/1.43 tff(1227,plain,
% 1.23/1.43 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1128, 1226])).
% 1.23/1.43 tff(1228,plain,
% 1.23/1.43 (r(s(s(s(elem!1))), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[110, 96, 88])).
% 1.23/1.43 tff(1229,plain,
% 1.23/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1230,plain,
% 1.23/1.43 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1231,plain,
% 1.23/1.43 (((~![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(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1230])).
% 1.23/1.43 tff(1232,plain,
% 1.23/1.43 (((~![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(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1231, 1229])).
% 1.23/1.43 tff(1233,plain,
% 1.23/1.43 ((~![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)))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1234,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.23/1.43 tff(1235,plain,
% 1.23/1.43 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1234, 141, 1228, 130])).
% 1.23/1.43 tff(1236,plain,
% 1.23/1.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1237,plain,
% 1.23/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1238,plain,
% 1.23/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.23/1.43 tff(1239,plain,
% 1.23/1.43 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1238, 32])).
% 1.23/1.43 tff(1240,plain,
% 1.23/1.43 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1239, 1235, 305])).
% 1.23/1.43 tff(1241,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.43 tff(1242,plain,
% 1.23/1.43 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1241])).
% 1.23/1.43 tff(1243,plain,
% 1.23/1.43 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[255, 1242, 113, 1241])).
% 1.23/1.43 tff(1244,plain,
% 1.23/1.43 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1243])).
% 1.23/1.43 tff(1245,plain,
% 1.23/1.43 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.23/1.43 inference(symmetry,[status(thm)],[155])).
% 1.23/1.43 tff(1246,plain,
% 1.23/1.43 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1245, 1244, 113, 1241])).
% 1.23/1.43 tff(1247,plain,
% 1.23/1.43 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1241])).
% 1.23/1.43 tff(1248,plain,
% 1.23/1.43 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1247, 2])).
% 1.23/1.43 tff(1249,plain,
% 1.23/1.43 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1248])).
% 1.23/1.43 tff(1250,plain,
% 1.23/1.43 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[11, 1249])).
% 1.23/1.43 tff(1251,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1250, 1246])).
% 1.23/1.43 tff(1252,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1253,plain,
% 1.23/1.43 (s(s(s(elem!1))) = s(elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1252, 1240])).
% 1.23/1.43 tff(1254,plain,
% 1.23/1.43 (s(elem!1) = s(s(s(elem!1)))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1253])).
% 1.23/1.43 tff(1255,plain,
% 1.23/1.43 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1254, 1240])).
% 1.23/1.43 tff(1256,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1, 1255])).
% 1.23/1.43 tff(1257,plain,((s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1258,plain,
% 1.23/1.43 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1257, 1221, 1, 88])).
% 1.23/1.43 tff(1259,assumption,(~b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.43 tff(1260,plain,
% 1.23/1.43 (((~![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))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1261,plain,
% 1.23/1.43 ((~![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))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1262,plain,
% 1.23/1.43 ((~![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)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 1.23/1.43 tff(1263,plain,
% 1.23/1.43 ((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)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1262, 32])).
% 1.23/1.43 tff(1264,plain,
% 1.23/1.43 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1263, 1, 1259])).
% 1.23/1.43 tff(1265,plain,
% 1.23/1.43 ((s(elem!1) = elem!1) | r(s(elem!1), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[568, 32, 564])).
% 1.23/1.43 tff(1266,plain,
% 1.23/1.43 (r(s(elem!1), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1265, 105])).
% 1.23/1.43 tff(1267,plain,
% 1.23/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1268,plain,
% 1.23/1.43 (((~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), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1269,plain,
% 1.23/1.43 (((~![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), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1268])).
% 1.23/1.43 tff(1270,plain,
% 1.23/1.43 (((~![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), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1269, 1267])).
% 1.23/1.43 tff(1271,plain,
% 1.23/1.43 ((~![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)))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1272,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.23/1.43 tff(1273,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1272, 141, 1266, 130, 1264])).
% 1.23/1.43 tff(1274,plain,((s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | b(s(elem!1), elem!1) | b(s(elem!1), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1275,plain,
% 1.23/1.43 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1274, 564, 1, 130])).
% 1.23/1.43 tff(1276,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.43 tff(1277,plain,
% 1.23/1.43 (r(s(elem!1), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[570, 564, 105])).
% 1.23/1.43 tff(1278,plain,
% 1.23/1.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[577, 1277, 170])).
% 1.23/1.43 tff(1279,plain,
% 1.23/1.43 (b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[353, 1278, 11])).
% 1.23/1.43 tff(1280,plain,
% 1.23/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(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))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1281,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1282,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 1.23/1.43 tff(1283,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1282, 141, 572, 130, 406])).
% 1.23/1.43 tff(1284,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1285,plain,
% 1.23/1.43 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1284, 1277, 130])).
% 1.23/1.43 tff(1286,plain,
% 1.23/1.43 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[420, 1285, 7])).
% 1.23/1.43 tff(1287,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.23/1.43 tff(1288,plain,
% 1.23/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1289,plain,
% 1.23/1.43 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1290,plain,
% 1.23/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[1289])).
% 1.23/1.43 tff(1291,plain,
% 1.23/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1290, 1288])).
% 1.23/1.43 tff(1292,plain,
% 1.23/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1293,plain,
% 1.23/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.23/1.43 tff(1294,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1293, 245, 1287, 556, 1276, 10])).
% 1.23/1.43 tff(1295,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1296,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1295, 1286, 1279, 1276, 1275])).
% 1.23/1.43 tff(1297,plain,(b(s(elem!1), elem!1) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1298,plain,
% 1.23/1.43 (b(s(elem!1), elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1297, 1258, 1227, 1221, 111, 1])).
% 1.23/1.43 tff(1299,plain,
% 1.23/1.43 (s(s(s(elem!1))) = s(elem!1)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1252, 1241])).
% 1.23/1.43 tff(1300,plain,
% 1.23/1.43 (s(elem!1) = s(s(s(elem!1)))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1299])).
% 1.23/1.43 tff(1301,plain,
% 1.23/1.43 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[1300, 1241])).
% 1.23/1.43 tff(1302,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1, 1301])).
% 1.23/1.43 tff(1303,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1304,plain,
% 1.23/1.43 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1303, 1])).
% 1.23/1.43 tff(1305,plain,
% 1.23/1.43 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.23/1.43 inference(commutativity,[status(thm)],[])).
% 1.23/1.43 tff(1306,plain,
% 1.23/1.43 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.23/1.43 inference(symmetry,[status(thm)],[1305])).
% 1.23/1.43 tff(1307,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.23/1.43 tff(1308,plain,
% 1.23/1.43 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 1.23/1.43 tff(1309,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.43 tff(1310,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1309, 1308])).
% 1.23/1.43 tff(1311,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(1312,plain,
% 1.23/1.43 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1311, 1304])).
% 1.23/1.43 tff(1313,plain,
% 1.23/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(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))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1314,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1315,plain,
% 1.23/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.23/1.43 tff(1316,plain,
% 1.23/1.43 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1315, 141, 111, 1221])).
% 1.23/1.43 tff(1317,plain,
% 1.23/1.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(1318,plain,
% 1.23/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(1319,plain,
% 1.23/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.23/1.44 tff(1320,plain,
% 1.23/1.44 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1319, 32])).
% 1.23/1.44 tff(1321,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1320, 1316, 1312])).
% 1.23/1.44 tff(1322,plain,
% 1.23/1.44 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1211])).
% 1.23/1.44 tff(1323,plain,
% 1.23/1.44 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.23/1.44 inference(commutativity,[status(thm)],[])).
% 1.23/1.44 tff(1324,plain,
% 1.23/1.44 ((elem!1 = s(z)) <=> (elem!1 = s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1211])).
% 1.23/1.44 tff(1325,plain,
% 1.23/1.44 ((elem!1 = s(z)) <=> (s(elem!1) = elem!1)),
% 1.23/1.44 inference(transitivity,[status(thm)],[1324, 1323])).
% 1.23/1.44 tff(1326,plain,
% 1.23/1.44 ((s(elem!1) = elem!1) <=> (elem!1 = s(z))),
% 1.23/1.44 inference(symmetry,[status(thm)],[1325])).
% 1.23/1.44 tff(1327,plain,
% 1.23/1.44 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1326])).
% 1.23/1.44 tff(1328,plain,
% 1.23/1.44 (~(elem!1 = s(z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[105, 1327])).
% 1.23/1.44 tff(1329,plain,
% 1.23/1.44 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.44 tff(1330,plain,
% 1.23/1.44 (r(elem!1, s(elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[268, 1329])).
% 1.23/1.44 tff(1331,plain,
% 1.23/1.44 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[58])).
% 1.23/1.44 tff(1332,plain,
% 1.23/1.44 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 1.23/1.44 inference(symmetry,[status(thm)],[1331])).
% 1.23/1.44 tff(1333,plain,
% 1.23/1.44 (r(elem!1, s(z)) <=> r(z, s(elem!1))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1329, 1332])).
% 1.23/1.44 tff(1334,plain,
% 1.23/1.44 (r(z, s(elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[268, 1333])).
% 1.23/1.44 tff(1335,plain,
% 1.23/1.44 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.23/1.44 inference(monotonicity,[status(thm)],[58])).
% 1.23/1.44 tff(1336,plain,
% 1.23/1.44 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.23/1.44 inference(symmetry,[status(thm)],[1335])).
% 1.23/1.44 tff(1337,plain,
% 1.23/1.44 (r(s(s(s(elem!1))), z)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[170, 1336])).
% 1.23/1.44 tff(1338,plain,
% 1.23/1.44 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.44 tff(1339,plain,
% 1.23/1.44 (~r(s(s(s(elem!1))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[276, 268, 170])).
% 1.23/1.44 tff(1340,plain,
% 1.23/1.44 (b(s(s(s(elem!1))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[265, 1339])).
% 1.23/1.44 tff(1341,plain,
% 1.23/1.44 (b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1340, 1338])).
% 1.23/1.44 tff(1342,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.23/1.44 tff(1343,plain,
% 1.23/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), 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(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1344,plain,
% 1.23/1.44 (((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1345,plain,
% 1.23/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1344])).
% 1.23/1.44 tff(1346,plain,
% 1.23/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1345, 1343])).
% 1.23/1.44 tff(1347,plain,
% 1.23/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1348,plain,
% 1.23/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.23/1.44 tff(1349,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1348, 141, 1342, 106, 406])).
% 1.23/1.44 tff(1350,plain,((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1351,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1350, 106, 1342])).
% 1.23/1.44 tff(1352,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[420, 1351, 164])).
% 1.23/1.44 tff(1353,plain,
% 1.23/1.44 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1295, 1352, 1287, 556])).
% 1.23/1.44 tff(1354,plain,
% 1.23/1.44 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1239, 1353, 1309])).
% 1.23/1.44 tff(1355,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.23/1.44 tff(1356,plain,
% 1.23/1.44 (((~![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(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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1357,plain,
% 1.23/1.44 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1358,plain,
% 1.23/1.44 (((~![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(elem!1))), z)) | (~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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1357])).
% 1.23/1.44 tff(1359,plain,
% 1.23/1.44 (((~![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(elem!1))), z)) | (~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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1358, 1356])).
% 1.23/1.44 tff(1360,plain,
% 1.23/1.44 ((~![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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1361,plain,
% 1.23/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.23/1.44 tff(1362,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1361, 141, 1355, 1354, 106])).
% 1.23/1.44 tff(1363,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1364,plain,
% 1.23/1.44 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1363, 1341, 106, 1304, 1337, 7, 1334])).
% 1.23/1.44 tff(1365,plain,
% 1.23/1.44 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1263, 1364, 1])).
% 1.23/1.44 tff(1366,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.44 tff(1367,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.23/1.44 tff(1368,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.44 tff(1369,plain,
% 1.23/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(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), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1370,plain,
% 1.23/1.44 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1371,plain,
% 1.23/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(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(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1370])).
% 1.23/1.44 tff(1372,plain,
% 1.23/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(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(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1371, 1369])).
% 1.23/1.44 tff(1373,plain,
% 1.23/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1374,plain,
% 1.23/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.23/1.44 tff(1375,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1374, 141, 1368, 1367, 1366])).
% 1.23/1.44 tff(1376,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1377,plain,
% 1.23/1.44 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1376, 1365, 1330])).
% 1.23/1.44 tff(1378,plain,
% 1.23/1.44 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.44 inference(monotonicity,[status(thm)],[58])).
% 1.23/1.44 tff(1379,plain,
% 1.23/1.44 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[106, 1378])).
% 1.23/1.44 tff(1380,plain,
% 1.23/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(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(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1381,plain,
% 1.23/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1382,plain,
% 1.23/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 1.23/1.44 tff(1383,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1382, 141, 1367, 130, 406])).
% 1.23/1.44 tff(1384,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1385,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1384, 1330, 1379])).
% 1.23/1.44 tff(1386,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[420, 1385, 7])).
% 1.23/1.44 tff(1387,plain,
% 1.23/1.44 (b(s(elem!1), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1274, 1364, 1, 1379])).
% 1.23/1.44 tff(1388,plain,
% 1.23/1.44 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.23/1.44 inference(symmetry,[status(thm)],[1338])).
% 1.23/1.44 tff(1389,plain,
% 1.23/1.44 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1388])).
% 1.23/1.44 tff(1390,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.44 tff(1391,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1392,plain,
% 1.23/1.44 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1393,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1392])).
% 1.23/1.44 tff(1394,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1393, 1391])).
% 1.23/1.44 tff(1395,plain,
% 1.23/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1396,plain,
% 1.23/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.23/1.44 tff(1397,plain,
% 1.23/1.44 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1396, 245, 1390, 308, 1276, 10])).
% 1.23/1.44 tff(1398,plain,
% 1.23/1.44 (~b(s(s(s(elem!1))), s(z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1397, 1389])).
% 1.23/1.44 tff(1399,plain,
% 1.23/1.44 (b(z, s(z)) <=> b(z, s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.44 tff(1400,plain,
% 1.23/1.44 (b(z, s(elem!1)) <=> b(z, s(z))),
% 1.23/1.44 inference(symmetry,[status(thm)],[1399])).
% 1.23/1.44 tff(1401,plain,
% 1.23/1.44 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[58])).
% 1.23/1.44 tff(1402,plain,
% 1.23/1.44 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 1.23/1.44 inference(symmetry,[status(thm)],[1401])).
% 1.23/1.44 tff(1403,plain,
% 1.23/1.44 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.23/1.44 tff(1404,plain,
% 1.23/1.44 ((~b(elem!1, s(elem!1))) <=> (~b(z, s(z)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1403])).
% 1.23/1.44 tff(1405,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1406,plain,
% 1.23/1.44 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1407,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1406])).
% 1.23/1.44 tff(1408,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1407, 1405])).
% 1.23/1.44 tff(1409,plain,
% 1.23/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1410,plain,
% 1.23/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.23/1.44 tff(1411,plain,
% 1.23/1.44 (~b(elem!1, s(elem!1))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1410, 245, 1390, 308, 10])).
% 1.23/1.44 tff(1412,plain,
% 1.23/1.44 (~b(z, s(z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1411, 1404])).
% 1.23/1.44 tff(1413,plain,
% 1.23/1.44 ((z = s(z)) <=> (s(z) = z)),
% 1.23/1.44 inference(commutativity,[status(thm)],[])).
% 1.23/1.44 tff(1414,plain,
% 1.23/1.44 ((s(z) = z) <=> (z = s(z))),
% 1.23/1.44 inference(symmetry,[status(thm)],[1413])).
% 1.23/1.44 tff(1415,plain,
% 1.23/1.44 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1414])).
% 1.23/1.44 tff(1416,plain,
% 1.23/1.44 (~(z = s(z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[228, 1415])).
% 1.23/1.44 tff(1417,plain,
% 1.23/1.44 (((~![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)))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1418,plain,
% 1.23/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1419,plain,
% 1.23/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.23/1.44 tff(1420,plain,
% 1.23/1.44 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1419, 32])).
% 1.23/1.44 tff(1421,plain,
% 1.23/1.44 (b(z, s(z)) | r(z, s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1420, 1416])).
% 1.23/1.44 tff(1422,plain,
% 1.23/1.44 (r(z, s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1421, 1412])).
% 1.23/1.44 tff(1423,plain,
% 1.23/1.44 (r(z, s(z)) <=> r(z, s(elem!1))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.44 tff(1424,plain,
% 1.23/1.44 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1423, 1331])).
% 1.23/1.44 tff(1425,plain,
% 1.23/1.44 (r(elem!1, s(elem!1))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1422, 1424])).
% 1.23/1.44 tff(1426,plain,
% 1.23/1.44 (~(s(elem!1) = elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[104, 102])).
% 1.23/1.44 tff(1427,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.23/1.44 tff(1428,plain,
% 1.23/1.44 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1376, 1366, 1367])).
% 1.23/1.44 tff(1429,plain,
% 1.23/1.44 (((~![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))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1430,plain,
% 1.23/1.44 ((~![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))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1431,plain,
% 1.23/1.44 ((~![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)))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.23/1.44 tff(1432,plain,
% 1.23/1.44 ((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)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1431, 32])).
% 1.23/1.44 tff(1433,plain,
% 1.23/1.44 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1432, 1428, 399])).
% 1.23/1.44 tff(1434,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1435,plain,
% 1.23/1.44 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(1436,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[1435])).
% 1.23/1.44 tff(1437,plain,
% 1.23/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[1436, 1434])).
% 1.23/1.44 tff(1438,plain,
% 1.23/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(1439,plain,
% 1.23/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 1.23/1.44 tff(1440,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1439, 245, 1390, 308, 1427, 1276, 10])).
% 1.23/1.44 tff(1441,plain,((~b(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1442,plain,
% 1.23/1.44 (~b(s(elem!1), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1441, 1433, 1427, 1276, 10])).
% 1.23/1.44 tff(1443,plain,
% 1.23/1.44 (r(s(elem!1), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[568, 32, 1442, 169])).
% 1.23/1.44 tff(1444,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1272, 141, 1443, 130, 1366])).
% 1.23/1.44 tff(1445,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (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)))), s(elem!1))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(1446,plain,
% 1.23/1.44 (~b(s(s(s(elem!1))), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1445, 1276, 1426, 1366, 10, 130, 399, 1425])).
% 1.23/1.44 tff(1447,plain,
% 1.23/1.44 (r(s(s(s(elem!1))), elem!1)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[110, 1446, 102])).
% 1.23/1.44 tff(1448,plain,
% 1.23/1.44 (r(s(s(s(elem!1))), z)),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[1447, 1336])).
% 1.23/1.45 tff(1449,assumption,(r(z, s(z))), introduced(assumption)).
% 1.23/1.45 tff(1450,plain,
% 1.23/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1451,plain,
% 1.23/1.45 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1452,plain,
% 1.23/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1451])).
% 1.23/1.45 tff(1453,plain,
% 1.23/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1452, 1450])).
% 1.23/1.45 tff(1454,plain,
% 1.23/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1455,plain,
% 1.23/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 1.23/1.45 tff(1456,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1455, 141, 1355, 267, 1449])).
% 1.23/1.45 tff(1457,plain,((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(1458,plain,
% 1.23/1.45 (~r(s(s(s(elem!1))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1457, 1448, 1422])).
% 1.23/1.45 tff(1459,plain,
% 1.23/1.45 (b(s(s(s(elem!1))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[265, 1458])).
% 1.23/1.45 tff(1460,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1459, 1398])).
% 1.23/1.45 tff(1461,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(z) = s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(1462,plain,
% 1.23/1.45 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1461, 1387, 39, 1386, 1276, 96, 1365, 1379, 67])).
% 1.23/1.45 tff(1463,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1432, 1462, 1377, 67])).
% 1.23/1.45 tff(1464,plain,((~r(elem!1, s(z))) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(1465,plain,
% 1.23/1.45 (~r(elem!1, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1464, 1211, 1258, 1, 106, 111])).
% 1.23/1.45 tff(1466,plain,
% 1.23/1.45 (b(elem!1, s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[281, 1465, 1328])).
% 1.23/1.45 tff(1467,plain,
% 1.23/1.45 (b(elem!1, s(elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1466, 1322])).
% 1.23/1.45 tff(1468,plain,
% 1.23/1.45 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1216])).
% 1.23/1.45 tff(1469,plain,
% 1.23/1.45 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.23/1.45 inference(symmetry,[status(thm)],[1468])).
% 1.23/1.45 tff(1470,plain,
% 1.23/1.45 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.45 inference(symmetry,[status(thm)],[770])).
% 1.23/1.45 tff(1471,plain,
% 1.23/1.45 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1219])).
% 1.23/1.45 tff(1472,plain,
% 1.23/1.45 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1471, 770])).
% 1.23/1.45 tff(1473,plain,
% 1.23/1.45 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.45 inference(transitivity,[status(thm)],[1472, 1470])).
% 1.23/1.45 tff(1474,plain,
% 1.23/1.45 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1473])).
% 1.23/1.45 tff(1475,plain,
% 1.23/1.45 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[734, 1474])).
% 1.23/1.45 tff(1476,plain,
% 1.23/1.45 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1216, 1219])).
% 1.23/1.45 tff(1477,plain,
% 1.23/1.45 (elem!1 = z),
% 1.23/1.45 inference(symmetry,[status(thm)],[1219])).
% 1.23/1.45 tff(1478,plain,
% 1.23/1.45 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1477])).
% 1.23/1.45 tff(1479,plain,
% 1.23/1.45 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.23/1.45 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.23/1.45 tff(1480,plain,
% 1.23/1.45 ((~r(s(s(s(s(s(elem!1))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1479])).
% 1.23/1.45 tff(1481,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.45 tff(1482,plain,
% 1.23/1.45 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1481])).
% 1.23/1.45 tff(1483,plain,
% 1.23/1.45 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1482])).
% 1.23/1.45 tff(1484,plain,
% 1.23/1.45 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1483])).
% 1.23/1.45 tff(1485,plain,
% 1.23/1.45 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[318])).
% 1.23/1.45 tff(1486,plain,
% 1.23/1.45 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1485, 1484, 113])).
% 1.23/1.45 tff(1487,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.45 tff(1488,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1487, 1486])).
% 1.23/1.45 tff(1489,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(1490,plain,
% 1.23/1.45 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1489, 1312])).
% 1.23/1.45 tff(1491,plain,
% 1.23/1.45 (s(s(z)) = s(s(elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.45 tff(1492,plain,
% 1.23/1.45 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1491])).
% 1.23/1.45 tff(1493,plain,
% 1.23/1.45 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1492])).
% 1.23/1.45 tff(1494,plain,
% 1.23/1.45 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1493])).
% 1.23/1.45 tff(1495,plain,
% 1.23/1.45 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1494])).
% 1.23/1.45 tff(1496,plain,
% 1.23/1.45 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1492])).
% 1.23/1.45 tff(1497,plain,
% 1.23/1.45 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1496, 1495])).
% 1.23/1.45 tff(1498,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1497])).
% 1.23/1.45 tff(1499,plain,
% 1.23/1.45 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1496, 1495])).
% 1.23/1.45 tff(1500,plain,
% 1.23/1.45 ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1499])).
% 1.23/1.45 tff(1501,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.23/1.45 tff(1502,plain,
% 1.23/1.45 (((~![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(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(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))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1503,plain,
% 1.23/1.45 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1504,plain,
% 1.23/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1503])).
% 1.23/1.45 tff(1505,plain,
% 1.23/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1504, 1502])).
% 1.23/1.45 tff(1506,plain,
% 1.23/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1507,plain,
% 1.23/1.45 ((~![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(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.23/1.45 tff(1508,plain,
% 1.23/1.45 ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1507, 141, 170])).
% 1.23/1.45 tff(1509,plain,
% 1.23/1.45 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1508, 1501])).
% 1.23/1.45 tff(1510,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1509, 1500])).
% 1.23/1.45 tff(1511,plain,
% 1.23/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1512,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1513,plain,
% 1.23/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.23/1.45 tff(1514,plain,
% 1.23/1.45 ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1513, 32])).
% 1.23/1.45 tff(1515,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1514, 704])).
% 1.23/1.45 tff(1516,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1515, 1510])).
% 1.23/1.45 tff(1517,plain,
% 1.23/1.45 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1516, 1498])).
% 1.23/1.45 tff(1518,plain,
% 1.23/1.45 (((~![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)))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1519,plain,
% 1.23/1.45 ((~![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)))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1520,plain,
% 1.23/1.45 ((~![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))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 1.23/1.45 tff(1521,plain,
% 1.23/1.45 ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1520, 141, 130])).
% 1.23/1.45 tff(1522,plain,
% 1.23/1.45 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1521, 1501])).
% 1.23/1.45 tff(1523,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.45 tff(1524,plain,
% 1.23/1.45 (((~![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))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1525,plain,
% 1.23/1.45 ((~![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))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1526,plain,
% 1.23/1.45 ((~![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)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 1.23/1.45 tff(1527,plain,
% 1.23/1.45 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1526, 32, 1523, 1522])).
% 1.23/1.45 tff(1528,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.45 tff(1529,plain,
% 1.23/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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))))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1530,plain,
% 1.23/1.45 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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(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(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)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1531,plain,
% 1.23/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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)))))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1530])).
% 1.23/1.45 tff(1532,plain,
% 1.23/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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))))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.23/1.45 tff(1533,plain,
% 1.23/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(s(s(s(elem!1))))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1534,plain,
% 1.23/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.23/1.45 tff(1535,plain,
% 1.23/1.45 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1534, 245, 1528, 1276, 1527])).
% 1.23/1.45 tff(1536,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1535, 1517])).
% 1.23/1.45 tff(1537,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(1538,plain,
% 1.23/1.45 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1537, 1211, 1321, 1258, 1490, 111, 1221])).
% 1.23/1.45 tff(1539,plain,
% 1.23/1.45 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1538, 1480])).
% 1.23/1.45 tff(1540,plain,
% 1.23/1.45 (b(s(s(s(s(s(z))))), elem!1)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[787, 1539, 1475])).
% 1.23/1.45 tff(1541,plain,
% 1.23/1.45 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1540, 1469])).
% 1.23/1.45 tff(1542,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.23/1.45 tff(1543,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.23/1.45 tff(1544,plain,
% 1.23/1.45 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.45 tff(1545,plain,
% 1.23/1.45 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1544])).
% 1.23/1.45 tff(1546,plain,
% 1.23/1.45 ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1545])).
% 1.23/1.45 tff(1547,plain,
% 1.23/1.45 ((s(s(s(s(s(s(elem!1)))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.45 inference(commutativity,[status(thm)],[])).
% 1.23/1.45 tff(1548,plain,
% 1.23/1.45 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.45 inference(symmetry,[status(thm)],[1547])).
% 1.23/1.45 tff(1549,plain,
% 1.23/1.45 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.45 inference(monotonicity,[status(thm)],[58])).
% 1.23/1.45 tff(1550,plain,
% 1.23/1.45 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1549, 1547])).
% 1.23/1.45 tff(1551,plain,
% 1.23/1.45 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.45 inference(transitivity,[status(thm)],[1550, 1548])).
% 1.23/1.45 tff(1552,plain,
% 1.23/1.45 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1551])).
% 1.23/1.45 tff(1553,plain,
% 1.23/1.45 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1554,plain,
% 1.23/1.45 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1553, 20])).
% 1.23/1.45 tff(1555,plain,
% 1.23/1.45 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1554, 1552])).
% 1.23/1.45 tff(1556,plain,
% 1.23/1.45 (s(elem!1) = s(z)),
% 1.23/1.45 inference(symmetry,[status(thm)],[39])).
% 1.23/1.45 tff(1557,plain,
% 1.23/1.45 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1556])).
% 1.23/1.45 tff(1558,plain,
% 1.23/1.45 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(z) = s(s(s(elem!1))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1557, 1121])).
% 1.23/1.45 tff(1559,plain,
% 1.23/1.45 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1558])).
% 1.23/1.45 tff(1560,plain,
% 1.23/1.45 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1559])).
% 1.23/1.45 tff(1561,plain,
% 1.23/1.45 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1128, 1560])).
% 1.23/1.45 tff(1562,plain,
% 1.23/1.45 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[331, 1561])).
% 1.23/1.45 tff(1563,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))), introduced(assumption)).
% 1.23/1.45 tff(1564,plain,
% 1.23/1.45 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1563, 1492])).
% 1.23/1.45 tff(1565,plain,
% 1.23/1.45 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1564])).
% 1.23/1.45 tff(1566,plain,
% 1.23/1.45 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1565])).
% 1.23/1.45 tff(1567,plain,
% 1.23/1.45 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[255, 1566, 320])).
% 1.23/1.45 tff(1568,plain,
% 1.23/1.45 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1567])).
% 1.23/1.45 tff(1569,plain,
% 1.23/1.45 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1245, 1568, 318])).
% 1.23/1.45 tff(1570,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1, 1569])).
% 1.23/1.45 tff(1571,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(1572,plain,
% 1.23/1.45 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1571, 39, 1])).
% 1.23/1.45 tff(1573,plain,
% 1.23/1.45 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1495])).
% 1.23/1.45 tff(1574,plain,
% 1.23/1.45 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1573])).
% 1.23/1.45 tff(1575,plain,
% 1.23/1.45 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.45 tff(1576,plain,
% 1.23/1.45 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1494, 39])).
% 1.23/1.45 tff(1577,plain,
% 1.23/1.45 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.23/1.45 inference(symmetry,[status(thm)],[1576])).
% 1.23/1.45 tff(1578,plain,
% 1.23/1.45 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1577])).
% 1.23/1.45 tff(1579,plain,
% 1.23/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), 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(X0, 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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1580,plain,
% 1.23/1.45 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1581,plain,
% 1.23/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[1580])).
% 1.23/1.45 tff(1582,plain,
% 1.23/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.45 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.23/1.45 tff(1583,plain,
% 1.23/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(1584,plain,
% 1.23/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.23/1.45 tff(1585,plain,
% 1.23/1.45 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1584, 245, 308, 1103])).
% 1.23/1.45 tff(1586,plain,
% 1.23/1.45 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1585, 1543])).
% 1.23/1.45 tff(1587,plain,
% 1.23/1.45 (~b(s(s(s(s(s(z))))), s(z))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1586, 1578])).
% 1.23/1.45 tff(1588,plain,
% 1.23/1.45 (r(s(s(s(s(s(z))))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[809, 1587])).
% 1.23/1.45 tff(1589,plain,
% 1.23/1.45 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1588, 1575])).
% 1.23/1.45 tff(1590,plain,
% 1.23/1.45 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[1589, 1574])).
% 1.23/1.45 tff(1591,plain,
% 1.23/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), 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(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(1592,plain,
% 1.23/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(1593,plain,
% 1.23/1.46 ((~![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(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.23/1.46 tff(1594,plain,
% 1.23/1.46 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1593, 141, 406, 1590])).
% 1.23/1.46 tff(1595,plain,
% 1.23/1.46 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1526, 32, 1490, 1594])).
% 1.23/1.46 tff(1596,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.46 tff(1597,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.46 tff(1598,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1599,plain,
% 1.23/1.46 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1600,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1599])).
% 1.23/1.46 tff(1601,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[1600, 1598])).
% 1.23/1.46 tff(1602,plain,
% 1.23/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(1603,plain,
% 1.23/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.23/1.46 tff(1604,plain,
% 1.23/1.46 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1603, 245, 1528, 1276, 1597, 1596])).
% 1.23/1.46 tff(1605,plain,
% 1.23/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1606,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(1607,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 1.23/1.46 tff(1608,plain,
% 1.23/1.46 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1607, 32, 1542, 1604])).
% 1.23/1.46 tff(1609,plain,
% 1.23/1.46 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[1499])).
% 1.23/1.46 tff(1610,plain,
% 1.23/1.46 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1497])).
% 1.23/1.46 tff(1611,plain,
% 1.23/1.46 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1534, 245, 1528, 1276, 1596])).
% 1.23/1.46 tff(1612,plain,
% 1.23/1.46 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 1.23/1.46 tff(1613,plain,
% 1.23/1.46 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1515, 1612])).
% 1.23/1.46 tff(1614,plain,
% 1.23/1.46 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1613, 1609])).
% 1.23/1.46 tff(1615,plain,
% 1.23/1.46 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1492])).
% 1.23/1.46 tff(1616,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))), introduced(assumption)).
% 1.23/1.46 tff(1617,plain,
% 1.23/1.46 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1496])).
% 1.23/1.46 tff(1618,plain,
% 1.23/1.46 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1617])).
% 1.23/1.46 tff(1619,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1620,plain,
% 1.23/1.46 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1621,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1620])).
% 1.23/1.46 tff(1622,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.23/1.46 tff(1623,plain,
% 1.23/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(1624,plain,
% 1.23/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.23/1.46 tff(1625,plain,
% 1.23/1.46 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1624, 245, 1528, 1276, 1597])).
% 1.23/1.46 tff(1626,plain,
% 1.23/1.46 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1625, 1618])).
% 1.23/1.46 tff(1627,plain,
% 1.23/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1628,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(1629,plain,
% 1.23/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.23/1.46 tff(1630,plain,
% 1.23/1.46 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1629, 32])).
% 1.23/1.46 tff(1631,plain,
% 1.23/1.46 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1630, 1626, 1616])).
% 1.23/1.46 tff(1632,plain,
% 1.23/1.46 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1631, 1615])).
% 1.23/1.46 tff(1633,plain,
% 1.23/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(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(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1634,plain,
% 1.23/1.46 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1635,plain,
% 1.23/1.46 (((~![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(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1634])).
% 1.23/1.46 tff(1636,plain,
% 1.23/1.46 (((~![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(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[1635, 1633])).
% 1.23/1.46 tff(1637,plain,
% 1.23/1.46 ((~![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(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(1638,plain,
% 1.23/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 1.23/1.46 tff(1639,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1638, 141, 1632, 1614, 1608])).
% 1.23/1.46 tff(1640,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (s(s(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(1641,plain,
% 1.23/1.46 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1640, 1595, 1572, 1542, 1528, 1276, 39])).
% 1.23/1.46 tff(1642,plain,
% 1.23/1.46 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[501, 1641, 1562])).
% 1.23/1.46 tff(1643,plain,
% 1.23/1.46 (elem!1 = z),
% 1.23/1.46 inference(symmetry,[status(thm)],[58])).
% 1.23/1.46 tff(1644,plain,
% 1.23/1.46 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1643])).
% 1.23/1.46 tff(1645,plain,
% 1.23/1.46 (b(z, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[1644])).
% 1.23/1.46 tff(1646,plain,
% 1.23/1.46 (b(z, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[58, 1495])).
% 1.23/1.46 tff(1647,plain,
% 1.23/1.46 (b(elem!1, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[1646])).
% 1.23/1.46 tff(1648,plain,
% 1.23/1.46 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[1647, 1645])).
% 1.23/1.46 tff(1649,plain,
% 1.23/1.46 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[58])).
% 1.23/1.46 tff(1650,plain,
% 1.23/1.46 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[1649, 770])).
% 1.23/1.46 tff(1651,plain,
% 1.23/1.46 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1650])).
% 1.23/1.46 tff(1652,plain,
% 1.23/1.46 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[734, 1651])).
% 1.23/1.46 tff(1653,plain,
% 1.23/1.46 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1495])).
% 1.23/1.46 tff(1654,plain,
% 1.23/1.46 ((~r(elem!1, s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1653])).
% 1.23/1.46 tff(1655,plain,
% 1.23/1.46 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1495, 1496])).
% 1.23/1.46 tff(1656,plain,
% 1.23/1.46 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[1655])).
% 1.23/1.46 tff(1657,plain,
% 1.23/1.46 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1495, 1496])).
% 1.23/1.46 tff(1658,plain,
% 1.23/1.46 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1657])).
% 1.23/1.46 tff(1659,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1660,plain,
% 1.23/1.46 (((~b(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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(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(s(s(elem!1))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(1661,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1660])).
% 1.23/1.46 tff(1662,plain,
% 1.23/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[1661, 1659])).
% 1.23/1.46 tff(1663,plain,
% 1.23/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(1664,plain,
% 1.23/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 1.23/1.46 tff(1665,plain,
% 1.23/1.46 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1664, 245, 1528, 1276, 1595])).
% 1.23/1.46 tff(1666,plain,
% 1.23/1.46 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1665, 1658])).
% 1.23/1.46 tff(1667,plain,
% 1.23/1.46 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[909, 1666])).
% 1.23/1.46 tff(1668,plain,
% 1.23/1.46 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1667, 1656])).
% 1.23/1.46 tff(1669,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.23/1.46 tff(1670,plain,
% 1.23/1.46 (s(s(s(elem!1))) = elem!1),
% 1.23/1.46 inference(symmetry,[status(thm)],[1669])).
% 1.23/1.46 tff(1671,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[102, 1670])).
% 1.23/1.46 tff(1672,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(1673,plain,
% 1.23/1.46 (~(elem!1 = s(s(s(elem!1))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1672, 96])).
% 1.23/1.46 tff(1674,plain,
% 1.23/1.46 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1534, 245, 1528, 1276, 1595])).
% 1.23/1.46 tff(1675,plain,
% 1.23/1.46 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1674, 1610])).
% 1.23/1.46 tff(1676,plain,
% 1.23/1.46 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1515, 1675])).
% 1.23/1.46 tff(1677,plain,
% 1.23/1.46 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[1676, 1609])).
% 1.23/1.46 tff(1678,plain,
% 1.23/1.46 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1556, 1495])).
% 1.23/1.46 tff(1679,plain,
% 1.23/1.46 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[1678])).
% 1.23/1.46 tff(1680,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[1494])).
% 1.23/1.46 tff(1681,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[1680])).
% 1.23/1.47 tff(1682,plain,
% 1.23/1.47 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1556])).
% 1.23/1.47 tff(1683,plain,
% 1.23/1.47 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[1682, 1681])).
% 1.23/1.47 tff(1684,plain,
% 1.23/1.47 ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~b(s(z), s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1683])).
% 1.23/1.47 tff(1685,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1686,plain,
% 1.23/1.47 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1687,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1686])).
% 1.23/1.47 tff(1688,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[1687, 1685])).
% 1.23/1.47 tff(1689,plain,
% 1.23/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1690,plain,
% 1.23/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 1.23/1.47 tff(1691,plain,
% 1.23/1.47 ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1690, 245, 308, 1103])).
% 1.23/1.47 tff(1692,plain,
% 1.23/1.47 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1691, 1543])).
% 1.23/1.47 tff(1693,plain,
% 1.23/1.47 (~b(s(z), s(s(s(s(s(z))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1692, 1684])).
% 1.23/1.47 tff(1694,plain,
% 1.23/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1695,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1696,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 1.23/1.47 tff(1697,plain,
% 1.23/1.47 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1696, 32])).
% 1.23/1.47 tff(1698,plain,
% 1.23/1.47 (b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1697, 702])).
% 1.23/1.47 tff(1699,plain,
% 1.23/1.47 (r(s(z), s(s(s(s(s(z))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1698, 1693])).
% 1.23/1.47 tff(1700,plain,
% 1.23/1.47 (r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1699, 1679])).
% 1.23/1.47 tff(1701,plain,
% 1.23/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(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(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1702,plain,
% 1.23/1.47 (((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1703,plain,
% 1.23/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1702])).
% 1.23/1.47 tff(1704,plain,
% 1.23/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[1703, 1701])).
% 1.23/1.47 tff(1705,plain,
% 1.23/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1706,plain,
% 1.23/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 1.23/1.47 tff(1707,plain,
% 1.23/1.47 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1706, 141, 1700])).
% 1.23/1.47 tff(1708,plain,
% 1.23/1.47 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1707, 1677])).
% 1.23/1.47 tff(1709,plain,
% 1.23/1.47 (b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[353, 1708, 1561])).
% 1.23/1.47 tff(1710,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), 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(X0, 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))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1711,plain,
% 1.23/1.47 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1712,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, 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))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1711])).
% 1.23/1.47 tff(1713,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, 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))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[1712, 1710])).
% 1.23/1.47 tff(1714,plain,
% 1.23/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1715,plain,
% 1.23/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1714, 1713])).
% 1.23/1.47 tff(1716,plain,
% 1.23/1.47 (~b(elem!1, s(s(s(elem!1))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1715, 245, 1709, 308, 1103])).
% 1.23/1.47 tff(1717,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.47 tff(1718,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.47 tff(1719,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.47 tff(1720,plain,
% 1.23/1.47 (((~![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)))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1721,plain,
% 1.23/1.47 ((~![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)))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1722,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 1.23/1.47 tff(1723,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1722, 32, 1719, 1718, 1717])).
% 1.23/1.47 tff(1724,plain,(b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(1725,plain,
% 1.23/1.47 (r(elem!1, s(s(s(elem!1))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1724, 1716, 1673])).
% 1.23/1.47 tff(1726,plain,
% 1.23/1.47 (((~![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(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(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1727,plain,
% 1.23/1.47 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1728,plain,
% 1.23/1.47 (((~![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(elem!1, s(s(s(elem!1))))) | (~r(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(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1727])).
% 1.23/1.47 tff(1729,plain,
% 1.23/1.47 (((~![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(elem!1, s(s(s(elem!1))))) | (~r(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(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[1728, 1726])).
% 1.23/1.47 tff(1730,plain,
% 1.23/1.47 ((~![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(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1731,plain,
% 1.23/1.47 ((~![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(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.23/1.47 tff(1732,plain,
% 1.23/1.47 ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1731, 141, 1725])).
% 1.23/1.47 tff(1733,plain,
% 1.23/1.47 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1732, 1668])).
% 1.23/1.47 tff(1734,plain,
% 1.23/1.47 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1733, 1654])).
% 1.23/1.47 tff(1735,plain,
% 1.23/1.47 (b(elem!1, s(s(s(s(s(z))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[720, 1734, 1652])).
% 1.23/1.47 tff(1736,plain,
% 1.23/1.47 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1735, 1648])).
% 1.23/1.47 tff(1737,plain,
% 1.23/1.47 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(commutativity,[status(thm)],[])).
% 1.23/1.47 tff(1738,plain,
% 1.23/1.47 ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[1737])).
% 1.23/1.47 tff(1739,plain,
% 1.23/1.47 ((~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1738])).
% 1.23/1.47 tff(1740,plain,
% 1.23/1.47 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1490, 1739])).
% 1.23/1.47 tff(1741,plain,
% 1.23/1.47 (((~![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(elem!1)))), s(s(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(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1742,plain,
% 1.23/1.47 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1743,plain,
% 1.23/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(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(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1742])).
% 1.23/1.47 tff(1744,plain,
% 1.23/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(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(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[1743, 1741])).
% 1.23/1.47 tff(1745,plain,
% 1.23/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1746,plain,
% 1.23/1.47 ((~![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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.23/1.47 tff(1747,plain,
% 1.23/1.47 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1746, 141, 406, 1590])).
% 1.23/1.47 tff(1748,plain,
% 1.23/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1749,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1750,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.23/1.47 tff(1751,plain,
% 1.23/1.47 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1750, 32, 1747])).
% 1.23/1.47 tff(1752,plain,
% 1.23/1.47 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1751, 1740])).
% 1.23/1.47 tff(1753,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1754,plain,
% 1.23/1.47 (((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1755,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[1754])).
% 1.23/1.47 tff(1756,plain,
% 1.23/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[1755, 1753])).
% 1.23/1.47 tff(1757,plain,
% 1.23/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1758,plain,
% 1.23/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 1.23/1.47 tff(1759,plain,
% 1.23/1.47 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1758, 245, 1543, 1752, 1736])).
% 1.23/1.47 tff(1760,plain,
% 1.23/1.47 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[1432, 1759, 67])).
% 1.23/1.47 tff(1761,plain,
% 1.23/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(1762,plain,
% 1.23/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(1763,plain,
% 1.23/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.23/1.47 tff(1764,plain,
% 1.23/1.47 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1763, 141, 1760, 1642])).
% 1.23/1.48 tff(1765,plain,
% 1.23/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1766,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1767,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 1.23/1.48 tff(1768,plain,
% 1.23/1.48 ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1767, 32])).
% 1.23/1.48 tff(1769,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1768, 1764, 1555])).
% 1.23/1.48 tff(1770,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1771,plain,
% 1.23/1.48 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1772,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1771])).
% 1.23/1.48 tff(1773,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[1772, 1770])).
% 1.23/1.48 tff(1774,plain,
% 1.23/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1775,plain,
% 1.23/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 1.23/1.48 tff(1776,plain,
% 1.23/1.48 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1775, 245, 308, 1103, 1769])).
% 1.23/1.48 tff(1777,plain,
% 1.23/1.48 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1776, 1546])).
% 1.23/1.48 tff(1778,plain,
% 1.23/1.48 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.48 tff(1779,plain,
% 1.23/1.48 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.48 inference(symmetry,[status(thm)],[1778])).
% 1.23/1.48 tff(1780,plain,
% 1.23/1.48 ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1779])).
% 1.23/1.48 tff(1781,plain,
% 1.23/1.48 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.48 tff(1782,plain,
% 1.23/1.48 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[39])).
% 1.23/1.48 tff(1783,plain,
% 1.23/1.48 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[1782])).
% 1.23/1.48 tff(1784,plain,
% 1.23/1.48 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1783])).
% 1.23/1.48 tff(1785,plain,
% 1.23/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1786,plain,
% 1.23/1.48 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1787,plain,
% 1.23/1.48 (((~![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(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1786])).
% 1.23/1.48 tff(1788,plain,
% 1.23/1.48 (((~![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(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[1787, 1785])).
% 1.23/1.48 tff(1789,plain,
% 1.23/1.48 ((~![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(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1790,plain,
% 1.23/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.23/1.48 tff(1791,plain,
% 1.23/1.48 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1790, 141, 1700])).
% 1.23/1.48 tff(1792,plain,
% 1.23/1.48 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1791, 1677])).
% 1.23/1.48 tff(1793,plain,
% 1.23/1.48 (~r(s(z), s(s(s(elem!1))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1792, 1784])).
% 1.23/1.48 tff(1794,plain,
% 1.23/1.48 (b(s(z), s(s(s(elem!1))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1133, 1793])).
% 1.23/1.48 tff(1795,plain,
% 1.23/1.48 (b(s(elem!1), s(s(s(elem!1))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1794, 1781])).
% 1.23/1.48 tff(1796,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1797,plain,
% 1.23/1.48 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(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(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1798,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1797])).
% 1.23/1.48 tff(1799,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.23/1.48 tff(1800,plain,
% 1.23/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1801,plain,
% 1.23/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.23/1.48 tff(1802,plain,
% 1.23/1.48 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1801, 245, 1709, 1795, 1528])).
% 1.23/1.48 tff(1803,plain,
% 1.23/1.48 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1263, 1802, 1])).
% 1.23/1.48 tff(1804,plain,
% 1.23/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1805,plain,
% 1.23/1.48 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1806,plain,
% 1.23/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1805])).
% 1.23/1.48 tff(1807,plain,
% 1.23/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[1806, 1804])).
% 1.23/1.48 tff(1808,plain,
% 1.23/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1809,plain,
% 1.23/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 1.23/1.48 tff(1810,plain,
% 1.23/1.48 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1809, 141, 1803, 1642])).
% 1.23/1.48 tff(1811,plain,
% 1.23/1.48 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1810, 1780])).
% 1.23/1.48 tff(1812,plain,
% 1.23/1.48 ((s(s(s(s(s(s(elem!1)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(commutativity,[status(thm)],[])).
% 1.23/1.48 tff(1813,plain,
% 1.23/1.48 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.23/1.48 inference(symmetry,[status(thm)],[1812])).
% 1.23/1.48 tff(1814,plain,
% 1.23/1.48 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(z)))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1813])).
% 1.23/1.48 tff(1815,plain,
% 1.23/1.48 (~(s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[465, 1814])).
% 1.23/1.48 tff(1816,plain,
% 1.23/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1817,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1818,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 1.23/1.48 tff(1819,plain,
% 1.23/1.48 ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1818, 32])).
% 1.23/1.48 tff(1820,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1819, 1815])).
% 1.23/1.48 tff(1821,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1820, 1811])).
% 1.23/1.48 tff(1822,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1821, 1777])).
% 1.23/1.48 tff(1823,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(1824,plain,
% 1.23/1.48 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1823, 1543, 308, 1103, 1542, 1528, 1276, 39, 1])).
% 1.23/1.48 tff(1825,plain,
% 1.23/1.48 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[420, 1824, 7])).
% 1.23/1.48 tff(1826,plain,
% 1.23/1.48 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1827,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1826])).
% 1.23/1.48 tff(1828,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[1827, 1405])).
% 1.23/1.48 tff(1829,plain,
% 1.23/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1830,plain,
% 1.23/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.23/1.48 tff(1831,plain,
% 1.23/1.48 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1830, 245, 308, 1103, 1825])).
% 1.23/1.48 tff(1832,plain,
% 1.23/1.48 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1432, 1831, 67])).
% 1.23/1.48 tff(1833,plain,
% 1.23/1.48 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[1657])).
% 1.23/1.48 tff(1834,plain,
% 1.23/1.48 ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1655])).
% 1.23/1.48 tff(1835,plain,
% 1.23/1.48 (((~![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(elem!1))))), 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(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1836,plain,
% 1.23/1.48 ((~![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(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(1837,plain,
% 1.23/1.48 ((~![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(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 1.23/1.48 tff(1838,plain,
% 1.23/1.48 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1837, 141, 371, 1590])).
% 1.23/1.48 tff(1839,plain,
% 1.23/1.48 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1838, 1834])).
% 1.23/1.48 tff(1840,plain,
% 1.23/1.48 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[909, 1839])).
% 1.23/1.48 tff(1841,plain,
% 1.23/1.48 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[1840, 1833])).
% 1.23/1.48 tff(1842,plain,
% 1.23/1.48 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(1843,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[1842])).
% 1.23/1.48 tff(1844,plain,
% 1.23/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[1843, 1659])).
% 1.23/1.48 tff(1845,plain,
% 1.23/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1846,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.23/1.49 tff(1847,plain,
% 1.23/1.49 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1846, 245, 1528, 1276, 1841])).
% 1.23/1.49 tff(1848,plain,
% 1.23/1.49 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1526, 32, 1847, 1490])).
% 1.23/1.49 tff(1849,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.49 tff(1850,plain,
% 1.23/1.49 (((~![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(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1851,plain,
% 1.23/1.49 ((~![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(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1852,plain,
% 1.23/1.49 ((~![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(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 1.23/1.49 tff(1853,plain,
% 1.23/1.49 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1852, 141, 529, 1849])).
% 1.23/1.49 tff(1854,plain,
% 1.23/1.49 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1607, 32, 1542, 1853])).
% 1.23/1.49 tff(1855,assumption,(~(s(s(s(s(s(s(elem!1)))))) = elem!1)), introduced(assumption)).
% 1.23/1.49 tff(1856,plain,
% 1.23/1.49 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1763, 141, 1368, 529])).
% 1.23/1.49 tff(1857,plain,
% 1.23/1.49 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1768, 1856, 1855])).
% 1.23/1.49 tff(1858,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1859,plain,
% 1.23/1.49 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1860,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[1859])).
% 1.23/1.49 tff(1861,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[1860, 1858])).
% 1.23/1.49 tff(1862,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1863,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.23/1.49 tff(1864,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1863, 245, 308, 1103, 1857, 1543, 1854])).
% 1.23/1.49 tff(1865,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(1866,plain,
% 1.23/1.49 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1865, 1848, 1103, 1543, 1542, 1555, 308, 1832])).
% 1.23/1.49 tff(1867,plain,
% 1.23/1.49 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[501, 1866, 1562])).
% 1.23/1.49 tff(1868,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1869,plain,
% 1.23/1.49 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1870,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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)))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[1869])).
% 1.23/1.49 tff(1871,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[1870, 1868])).
% 1.23/1.49 tff(1872,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1873,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(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)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 1.23/1.49 tff(1874,plain,
% 1.23/1.49 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1873, 245, 1528, 1276, 1841])).
% 1.23/1.49 tff(1875,plain,
% 1.23/1.49 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1750, 32, 1874])).
% 1.23/1.49 tff(1876,plain,
% 1.23/1.49 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1875, 1740])).
% 1.23/1.49 tff(1877,plain,
% 1.23/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1878,plain,
% 1.23/1.49 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1879,plain,
% 1.23/1.49 (((~![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(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(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), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[1878])).
% 1.23/1.49 tff(1880,plain,
% 1.23/1.49 (((~![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(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(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), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[1879, 1877])).
% 1.23/1.49 tff(1881,plain,
% 1.23/1.49 ((~![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(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1882,plain,
% 1.23/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 1.23/1.49 tff(1883,plain,
% 1.23/1.49 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1882, 141, 1700, 1876])).
% 1.23/1.49 tff(1884,plain,
% 1.23/1.49 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1263, 1883, 1])).
% 1.23/1.49 tff(1885,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1886,plain,
% 1.23/1.49 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(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(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(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(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1887,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(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(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[1886])).
% 1.23/1.49 tff(1888,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(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(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[1887, 1885])).
% 1.23/1.49 tff(1889,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(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(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1890,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 1.23/1.49 tff(1891,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1890, 245, 1884, 1276, 1825, 1867])).
% 1.23/1.49 tff(1892,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1891, 1618])).
% 1.23/1.49 tff(1893,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1630, 1892, 1572])).
% 1.23/1.49 tff(1894,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1893, 1615])).
% 1.23/1.49 tff(1895,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1896,plain,
% 1.23/1.49 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(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(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1897,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[1896])).
% 1.23/1.49 tff(1898,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[1897, 1895])).
% 1.23/1.49 tff(1899,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1900,plain,
% 1.23/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 1.23/1.49 tff(1901,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1900, 245, 1884, 1825, 1867])).
% 1.23/1.49 tff(1902,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1901, 1546])).
% 1.23/1.49 tff(1903,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1820, 1902])).
% 1.23/1.49 tff(1904,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1903, 1778])).
% 1.23/1.49 tff(1905,plain,
% 1.23/1.49 (((~![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(elem!1)))))), s(elem!1))) | (~r(s(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(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(1906,plain,
% 1.23/1.49 ((~![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(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(1907,plain,
% 1.23/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 1.23/1.49 tff(1908,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1907, 141, 371, 1904, 1894])).
% 1.23/1.49 tff(1909,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(1910,plain,
% 1.23/1.49 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[1909, 1543, 1276, 1103, 39, 1542, 308, 1, 1528])).
% 1.23/1.49 tff(1911,plain,
% 1.23/1.49 (b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[353, 1910, 1561])).
% 1.23/1.49 tff(1912,plain,
% 1.23/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(X0, 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)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(1913,plain,
% 1.23/1.50 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(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(elem!1))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(1914,plain,
% 1.23/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(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(X0, 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)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[1913])).
% 1.23/1.50 tff(1915,plain,
% 1.23/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(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(X0, 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)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.23/1.50 inference(transitivity,[status(thm)],[1914, 1912])).
% 1.23/1.50 tff(1916,plain,
% 1.23/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.23/1.50 inference(quant_inst,[status(thm)],[])).
% 1.23/1.50 tff(1917,plain,
% 1.23/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 1.23/1.50 tff(1918,plain,
% 1.23/1.50 ($false),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[1917, 245, 1911, 308, 1103, 1528, 1825])).
% 1.23/1.50 tff(1919,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.50 tff(1920,plain,
% 1.23/1.50 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[1919, 1541, 1467, 1321, 1258, 1211, 1298, 1])).
% 1.23/1.50 tff(1921,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.50 tff(1922,plain,
% 1.23/1.50 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[1921])).
% 1.33/1.50 tff(1923,plain,
% 1.33/1.50 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1922])).
% 1.33/1.50 tff(1924,plain,
% 1.33/1.50 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1921])).
% 1.33/1.50 tff(1925,plain,
% 1.33/1.50 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[1494, 1924, 1923])).
% 1.33/1.50 tff(1926,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[673, 1925])).
% 1.33/1.50 tff(1927,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(1928,plain,
% 1.33/1.50 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1927, 1920, 1211])).
% 1.33/1.50 tff(1929,plain,
% 1.33/1.50 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1928])).
% 1.33/1.50 tff(1930,plain,
% 1.33/1.50 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[1929, 1215])).
% 1.33/1.50 tff(1931,plain,
% 1.33/1.50 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1930])).
% 1.33/1.50 tff(1932,plain,
% 1.33/1.50 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1931])).
% 1.33/1.50 tff(1933,plain,
% 1.33/1.50 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[1485, 1932, 1218])).
% 1.33/1.50 tff(1934,plain,
% 1.33/1.50 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1933])).
% 1.33/1.50 tff(1935,plain,
% 1.33/1.50 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[1213, 206, 1934, 320, 1216])).
% 1.33/1.50 tff(1936,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[704, 1935])).
% 1.33/1.50 tff(1937,plain,(b(s(s(s(elem!1))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(elem!1)))), elem!1) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(1938,plain,
% 1.33/1.50 (~r(s(s(s(s(elem!1)))), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1937, 8, 90, 89, 88, 1])).
% 1.33/1.50 tff(1939,plain,
% 1.33/1.50 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.50 inference(commutativity,[status(thm)],[])).
% 1.33/1.50 tff(1940,plain,
% 1.33/1.50 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1939])).
% 1.33/1.50 tff(1941,plain,
% 1.33/1.50 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1940])).
% 1.33/1.50 tff(1942,plain,
% 1.33/1.50 ((~(s(s(s(s(elem!1)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[61])).
% 1.33/1.50 tff(1943,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.33/1.50 tff(1944,plain,
% 1.33/1.50 (b(s(s(s(s(elem!1)))), z) <=> b(elem!1, z)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[199])).
% 1.33/1.50 tff(1945,plain,
% 1.33/1.50 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.33/1.50 inference(symmetry,[status(thm)],[1944])).
% 1.33/1.50 tff(1946,plain,
% 1.33/1.50 ((~b(elem!1, z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1945])).
% 1.33/1.50 tff(1947,plain,
% 1.33/1.50 (~b(s(s(s(s(elem!1)))), z)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[89, 1946])).
% 1.33/1.50 tff(1948,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1943, 1947])).
% 1.33/1.50 tff(1949,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(1950,plain,
% 1.33/1.50 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1949, 1943, 89])).
% 1.33/1.50 tff(1951,plain,
% 1.33/1.50 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[1950, 1942])).
% 1.33/1.50 tff(1952,plain,
% 1.33/1.50 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[553])).
% 1.33/1.50 tff(1953,plain,
% 1.33/1.50 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1952])).
% 1.33/1.50 tff(1954,plain,
% 1.33/1.50 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[848])).
% 1.33/1.50 tff(1955,plain,
% 1.33/1.50 (elem!1 = s(s(s(s(elem!1))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[684, 1954, 157, 1953])).
% 1.33/1.50 tff(1956,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[399, 1955])).
% 1.33/1.50 tff(1957,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(1958,plain,
% 1.33/1.50 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1957, 1951])).
% 1.33/1.50 tff(1959,plain,
% 1.33/1.50 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[1958, 1941])).
% 1.33/1.50 tff(1960,plain,
% 1.33/1.50 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1323])).
% 1.33/1.50 tff(1961,plain,
% 1.33/1.50 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1960])).
% 1.33/1.50 tff(1962,plain,
% 1.33/1.50 (~(elem!1 = s(elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[105, 1961])).
% 1.33/1.50 tff(1963,plain,
% 1.33/1.50 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[114])).
% 1.33/1.50 tff(1964,plain,
% 1.33/1.50 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.33/1.50 inference(symmetry,[status(thm)],[1963])).
% 1.33/1.50 tff(1965,plain,
% 1.33/1.50 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1964])).
% 1.33/1.50 tff(1966,plain,
% 1.33/1.50 (~b(s(s(s(s(elem!1)))), z)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[8, 1965])).
% 1.33/1.50 tff(1967,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1943, 1966])).
% 1.33/1.50 tff(1968,plain,((~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(1969,plain,
% 1.33/1.50 (~(z = elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1968, 8, 1943])).
% 1.33/1.50 tff(1970,plain,
% 1.33/1.50 (~(elem!1 = z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[123, 1969])).
% 1.33/1.50 tff(1971,plain,
% 1.33/1.50 (r(elem!1, z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[128, 1970, 89])).
% 1.33/1.50 tff(1972,plain,
% 1.33/1.50 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[151, 8, 1950])).
% 1.33/1.50 tff(1973,plain,
% 1.33/1.50 (r(z, elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[175, 1969, 90])).
% 1.33/1.50 tff(1974,plain,
% 1.33/1.50 (~(s(z) = s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[57, 1969])).
% 1.33/1.50 tff(1975,plain,
% 1.33/1.50 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(1976,plain,
% 1.33/1.50 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(1977,plain,
% 1.33/1.50 (((~![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(z, elem!1)) | (~r(z, s(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1976])).
% 1.33/1.50 tff(1978,plain,
% 1.33/1.50 (((~![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(z, elem!1)) | (~r(z, s(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[1977, 1975])).
% 1.33/1.50 tff(1979,plain,
% 1.33/1.50 ((~![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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(1980,plain,
% 1.33/1.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.33/1.50 tff(1981,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1980, 141, 289, 310, 130])).
% 1.33/1.50 tff(1982,plain,((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(1983,plain,
% 1.33/1.50 (~r(z, s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1982, 289, 130])).
% 1.33/1.50 tff(1984,plain,
% 1.33/1.50 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.33/1.50 inference(commutativity,[status(thm)],[])).
% 1.33/1.50 tff(1985,plain,
% 1.33/1.50 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[1984])).
% 1.33/1.50 tff(1986,plain,
% 1.33/1.50 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1985])).
% 1.33/1.50 tff(1987,plain,
% 1.33/1.50 (~(z = s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[66, 1986])).
% 1.33/1.50 tff(1988,plain,
% 1.33/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(1989,plain,
% 1.33/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(1990,plain,
% 1.33/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.33/1.50 tff(1991,plain,
% 1.33/1.50 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1990, 32])).
% 1.33/1.50 tff(1992,plain,
% 1.33/1.50 (b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1991, 1987])).
% 1.33/1.50 tff(1993,plain,
% 1.33/1.50 (b(z, s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1992, 1983])).
% 1.33/1.50 tff(1994,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(1995,plain,
% 1.33/1.50 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(1996,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[1995])).
% 1.33/1.50 tff(1997,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[1996, 1994])).
% 1.33/1.50 tff(1998,plain,
% 1.33/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(1999,plain,
% 1.33/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.33/1.50 tff(2000,plain,
% 1.33/1.50 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1999, 245, 288, 1993, 1943])).
% 1.33/1.50 tff(2001,plain,
% 1.33/1.50 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[420, 2000, 7])).
% 1.33/1.50 tff(2002,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2003,plain,
% 1.33/1.50 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2004,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[2003])).
% 1.33/1.50 tff(2005,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[2004, 2002])).
% 1.33/1.50 tff(2006,plain,
% 1.33/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2007,plain,
% 1.33/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 1.33/1.50 tff(2008,plain,
% 1.33/1.50 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2007, 245, 288, 1993, 1943])).
% 1.33/1.50 tff(2009,plain,
% 1.33/1.50 (b(s(elem!1), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1274, 2008, 1, 130])).
% 1.33/1.50 tff(2010,plain,
% 1.33/1.50 (~r(elem!1, s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1384, 406, 130])).
% 1.33/1.50 tff(2011,plain,
% 1.33/1.50 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1086, 32, 2010])).
% 1.33/1.50 tff(2012,plain,
% 1.33/1.50 (b(elem!1, s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2011, 1962])).
% 1.33/1.50 tff(2013,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1257, 305, 1, 130])).
% 1.33/1.50 tff(2014,plain,
% 1.33/1.50 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1252, 11])).
% 1.33/1.50 tff(2015,plain,
% 1.33/1.50 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1239, 305, 2014])).
% 1.33/1.50 tff(2016,plain,
% 1.33/1.50 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[415, 2015, 406])).
% 1.33/1.50 tff(2017,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[353, 2016, 11])).
% 1.33/1.50 tff(2018,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2019,plain,
% 1.33/1.50 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(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(elem!1))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(2020,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[2019])).
% 1.33/1.50 tff(2021,plain,
% 1.33/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[2020, 2018])).
% 1.33/1.50 tff(2022,plain,
% 1.33/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(2023,plain,
% 1.33/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 1.33/1.51 tff(2024,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2023, 245, 2017, 308, 2013, 2012])).
% 1.33/1.51 tff(2025,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(2026,plain,
% 1.33/1.51 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2025, 2009, 11, 2001, 1, 130])).
% 1.33/1.51 tff(2027,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2028,plain,
% 1.33/1.51 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2029,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2028])).
% 1.33/1.51 tff(2030,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2029, 2027])).
% 1.33/1.51 tff(2031,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2032,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.33/1.51 tff(2033,plain,
% 1.33/1.51 (~b(s(s(s(elem!1))), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2032, 245, 1993, 2026, 1943])).
% 1.33/1.51 tff(2034,plain,
% 1.33/1.51 (r(s(s(s(elem!1))), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[37, 2033])).
% 1.33/1.51 tff(2035,plain,
% 1.33/1.51 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1311, 2014])).
% 1.33/1.51 tff(2036,plain,
% 1.33/1.51 (((~![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)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2037,plain,
% 1.33/1.51 (((~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)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2038,plain,
% 1.33/1.51 (((~![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))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2037])).
% 1.33/1.51 tff(2039,plain,
% 1.33/1.51 (((~![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)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2038, 2036])).
% 1.33/1.51 tff(2040,plain,
% 1.33/1.51 ((~![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)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2041,plain,
% 1.33/1.51 ((~![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))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 1.33/1.51 tff(2042,plain,
% 1.33/1.51 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2041, 141, 131, 2034])).
% 1.33/1.51 tff(2043,plain,
% 1.33/1.51 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[110, 2042, 96])).
% 1.33/1.51 tff(2044,plain,
% 1.33/1.51 (~r(elem!1, s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1384, 2001, 130])).
% 1.33/1.51 tff(2045,plain,
% 1.33/1.51 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1086, 32, 2044])).
% 1.33/1.51 tff(2046,plain,
% 1.33/1.51 (b(elem!1, s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2045, 1962])).
% 1.33/1.51 tff(2047,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2048,plain,
% 1.33/1.51 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2049,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2048])).
% 1.33/1.51 tff(2050,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2049, 2047])).
% 1.33/1.51 tff(2051,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2052,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 1.33/1.51 tff(2053,plain,
% 1.33/1.51 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2052, 245, 2046, 288, 1993, 2026])).
% 1.33/1.51 tff(2054,plain,
% 1.33/1.51 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2053, 2043])).
% 1.33/1.51 tff(2055,plain,
% 1.33/1.51 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[353, 2054, 11])).
% 1.33/1.51 tff(2056,plain,
% 1.33/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(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))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2057,plain,
% 1.33/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2058,plain,
% 1.33/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 1.33/1.51 tff(2059,plain,
% 1.33/1.51 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2058, 141, 2055, 2001])).
% 1.33/1.51 tff(2060,plain,
% 1.33/1.51 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1320, 2059, 2035])).
% 1.33/1.51 tff(2061,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2062,plain,
% 1.33/1.51 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2063,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2062])).
% 1.33/1.51 tff(2064,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2063, 2061])).
% 1.33/1.51 tff(2065,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2066,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 1.33/1.51 tff(2067,plain,
% 1.33/1.51 (~b(z, s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2066, 245, 1993, 2026, 1943])).
% 1.33/1.51 tff(2068,plain,
% 1.33/1.51 (r(z, s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[197, 2067])).
% 1.33/1.51 tff(2069,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.51 tff(2070,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.51 tff(2071,plain,
% 1.33/1.51 (((~![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))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2072,plain,
% 1.33/1.51 (((~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))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2073,plain,
% 1.33/1.51 (((~![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)))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2072])).
% 1.33/1.51 tff(2074,plain,
% 1.33/1.51 (((~![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))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2073, 2071])).
% 1.33/1.51 tff(2075,plain,
% 1.33/1.51 ((~![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)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2076,plain,
% 1.33/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.33/1.51 tff(2077,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2076, 141, 289, 2070, 2069])).
% 1.33/1.51 tff(2078,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(2079,plain,
% 1.33/1.51 (~r(elem!1, s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2078, 2068, 289])).
% 1.33/1.51 tff(2080,plain,
% 1.33/1.51 (b(elem!1, s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1724, 2079, 1673])).
% 1.33/1.51 tff(2081,plain,
% 1.33/1.51 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[11, 1941])).
% 1.33/1.51 tff(2082,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2083,plain,
% 1.33/1.51 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2084,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2083])).
% 1.33/1.51 tff(2085,plain,
% 1.33/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2084, 2082])).
% 1.33/1.51 tff(2086,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2087,plain,
% 1.33/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 1.33/1.51 tff(2088,plain,
% 1.33/1.51 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2087, 245, 2009, 2080, 288, 2026, 1943])).
% 1.33/1.51 tff(2089,plain,
% 1.33/1.51 (((~![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)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2090,plain,
% 1.33/1.51 ((~![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)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2091,plain,
% 1.33/1.51 ((~![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))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2090, 2089])).
% 1.33/1.51 tff(2092,plain,
% 1.33/1.51 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2091, 32, 2088])).
% 1.33/1.51 tff(2093,plain,
% 1.33/1.51 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2092, 2081])).
% 1.33/1.51 tff(2094,plain,
% 1.33/1.51 (((~![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))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2095,plain,
% 1.33/1.51 (((~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))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2096,plain,
% 1.33/1.51 (((~![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)))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[2095])).
% 1.33/1.51 tff(2097,plain,
% 1.33/1.51 (((~![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))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[2096, 2094])).
% 1.33/1.51 tff(2098,plain,
% 1.33/1.51 ((~![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))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(2099,plain,
% 1.33/1.51 ((~![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)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 1.33/1.51 tff(2100,plain,
% 1.33/1.51 (~r(elem!1, s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[2099, 141, 131, 220])).
% 1.33/1.51 tff(2101,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.51 tff(2102,plain,
% 1.33/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(2103,plain,
% 1.33/1.51 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2104,plain,
% 1.33/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2103])).
% 1.33/1.52 tff(2105,plain,
% 1.33/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2104, 2102])).
% 1.33/1.52 tff(2106,plain,
% 1.33/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2107,plain,
% 1.33/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.33/1.52 tff(2108,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2107, 141, 1355, 220, 1135])).
% 1.33/1.52 tff(2109,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2110,plain,
% 1.33/1.52 (~r(s(z), s(s(s(elem!1))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2109, 220, 1355])).
% 1.33/1.52 tff(2111,plain,
% 1.33/1.52 (b(s(z), s(s(s(elem!1))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[1133, 2110])).
% 1.33/1.52 tff(2112,plain,
% 1.33/1.52 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2041, 141, 131, 1355])).
% 1.33/1.52 tff(2113,plain,
% 1.33/1.52 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[110, 2112, 96])).
% 1.33/1.52 tff(2114,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2115,plain,
% 1.33/1.52 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2116,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2115])).
% 1.33/1.52 tff(2117,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.33/1.52 tff(2118,plain,
% 1.33/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2119,plain,
% 1.33/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.33/1.52 tff(2120,plain,
% 1.33/1.52 (~b(elem!1, s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2119, 245, 2113, 1103, 2111, 2101])).
% 1.33/1.52 tff(2121,plain,
% 1.33/1.52 (elem!1 = s(z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[281, 2120, 2100])).
% 1.33/1.52 tff(2122,plain,
% 1.33/1.52 (s(elem!1) = s(s(z))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2121])).
% 1.33/1.52 tff(2123,plain,
% 1.33/1.52 (s(s(elem!1)) = s(s(s(z)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2122])).
% 1.33/1.52 tff(2124,plain,
% 1.33/1.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2123])).
% 1.33/1.52 tff(2125,plain,
% 1.33/1.52 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2124])).
% 1.33/1.52 tff(2126,plain,
% 1.33/1.52 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2125])).
% 1.33/1.52 tff(2127,plain,
% 1.33/1.52 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2126])).
% 1.33/1.52 tff(2128,plain,
% 1.33/1.52 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2127])).
% 1.33/1.52 tff(2129,plain,
% 1.33/1.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2124])).
% 1.33/1.52 tff(2130,plain,
% 1.33/1.52 (s(s(z)) = s(elem!1)),
% 1.33/1.52 inference(symmetry,[status(thm)],[2122])).
% 1.33/1.52 tff(2131,plain,
% 1.33/1.52 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2130, 2129])).
% 1.33/1.52 tff(2132,plain,
% 1.33/1.52 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2131])).
% 1.33/1.52 tff(2133,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.52 tff(2134,plain,
% 1.33/1.52 (r(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 1.33/1.52 tff(2135,plain,
% 1.33/1.52 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.52 inference(commutativity,[status(thm)],[])).
% 1.33/1.52 tff(2136,plain,
% 1.33/1.52 ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2135])).
% 1.33/1.52 tff(2137,plain,
% 1.33/1.52 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2136])).
% 1.33/1.52 tff(2138,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.33/1.52 tff(2139,plain,
% 1.33/1.52 (s(elem!1) = s(s(z))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2138])).
% 1.33/1.52 tff(2140,plain,
% 1.33/1.52 (s(s(elem!1)) = s(s(s(z)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2139])).
% 1.33/1.52 tff(2141,plain,
% 1.33/1.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2140])).
% 1.33/1.52 tff(2142,plain,
% 1.33/1.52 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2141])).
% 1.33/1.52 tff(2143,plain,
% 1.33/1.52 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2142])).
% 1.33/1.52 tff(2144,plain,
% 1.33/1.52 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2145,plain,
% 1.33/1.52 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2144, 47])).
% 1.33/1.52 tff(2146,plain,
% 1.33/1.52 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2142])).
% 1.33/1.52 tff(2147,plain,
% 1.33/1.52 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[599])).
% 1.33/1.52 tff(2148,plain,
% 1.33/1.52 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2147])).
% 1.33/1.52 tff(2149,plain,
% 1.33/1.52 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2148])).
% 1.33/1.52 tff(2150,plain,
% 1.33/1.52 (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[604, 2149, 1218])).
% 1.33/1.52 tff(2151,plain,
% 1.33/1.52 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2150])).
% 1.33/1.52 tff(2152,plain,
% 1.33/1.52 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[1043, 2151, 320, 2146])).
% 1.33/1.52 tff(2153,plain,
% 1.33/1.52 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2152])).
% 1.33/1.52 tff(2154,plain,
% 1.33/1.52 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2139, 586, 2153, 2145, 2143])).
% 1.33/1.52 tff(2155,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[1, 2154])).
% 1.33/1.52 tff(2156,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2157,plain,
% 1.33/1.52 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2156, 2121, 1])).
% 1.33/1.52 tff(2158,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.33/1.52 tff(2159,plain,
% 1.33/1.52 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2158])).
% 1.33/1.52 tff(2160,plain,
% 1.33/1.52 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2159])).
% 1.33/1.52 tff(2161,plain,
% 1.33/1.52 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2160])).
% 1.33/1.52 tff(2162,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[673, 2161])).
% 1.33/1.52 tff(2163,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2164,plain,
% 1.33/1.52 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2163, 2157])).
% 1.33/1.52 tff(2165,plain,
% 1.33/1.52 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2164, 2137])).
% 1.33/1.52 tff(2166,plain,
% 1.33/1.52 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2130])).
% 1.33/1.52 tff(2167,plain,
% 1.33/1.52 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2166])).
% 1.33/1.52 tff(2168,plain,
% 1.33/1.52 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2121])).
% 1.33/1.52 tff(2169,plain,
% 1.33/1.52 (b(s(z), s(elem!1))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[1103, 2168])).
% 1.33/1.52 tff(2170,plain,
% 1.33/1.52 (b(s(z), s(s(z)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2169, 2167])).
% 1.33/1.52 tff(2171,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2129])).
% 1.33/1.52 tff(2172,plain,
% 1.33/1.52 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2171])).
% 1.33/1.52 tff(2173,plain,
% 1.33/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2174,plain,
% 1.33/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2175,plain,
% 1.33/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 1.33/1.52 tff(2176,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2175, 141, 1355, 220, 267])).
% 1.33/1.52 tff(2177,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(2178,plain,
% 1.33/1.52 (~r(s(s(s(elem!1))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2177, 220, 1355])).
% 1.33/1.52 tff(2179,plain,
% 1.33/1.52 (b(s(s(s(elem!1))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[265, 2178])).
% 1.33/1.52 tff(2180,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), s(z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2179, 2172])).
% 1.33/1.52 tff(2181,plain,
% 1.33/1.52 (r(z, elem!1) <=> r(z, s(z))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2121])).
% 1.33/1.52 tff(2182,plain,
% 1.33/1.52 (r(z, s(z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[289, 2181])).
% 1.33/1.52 tff(2183,plain,
% 1.33/1.52 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2125])).
% 1.33/1.52 tff(2184,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2185,plain,
% 1.33/1.52 (((~b(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))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2186,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2185])).
% 1.33/1.52 tff(2187,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.33/1.52 tff(2188,plain,
% 1.33/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2189,plain,
% 1.33/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.33/1.52 tff(2190,plain,
% 1.33/1.52 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2189, 245, 2113, 2111, 2101, 1528])).
% 1.33/1.52 tff(2191,plain,
% 1.33/1.52 (r(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[217, 2190])).
% 1.33/1.52 tff(2192,plain,
% 1.33/1.52 (r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2191, 2183])).
% 1.33/1.52 tff(2193,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.33/1.52 tff(2194,plain,
% 1.33/1.52 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2125])).
% 1.33/1.52 tff(2195,plain,
% 1.33/1.52 (b(s(s(s(s(s(z))))), z)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[1943, 2194])).
% 1.33/1.52 tff(2196,plain,
% 1.33/1.52 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2125])).
% 1.33/1.52 tff(2197,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.33/1.52 tff(2198,plain,
% 1.33/1.52 (b(z, s(s(s(s(s(z))))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 1.33/1.52 tff(2199,plain,
% 1.33/1.52 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2143])).
% 1.33/1.52 tff(2200,plain,
% 1.33/1.52 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[2199])).
% 1.33/1.52 tff(2201,plain,
% 1.33/1.52 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2143])).
% 1.33/1.52 tff(2202,plain,
% 1.33/1.52 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2201])).
% 1.33/1.52 tff(2203,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 1.33/1.52 tff(2204,plain,
% 1.33/1.52 (((~![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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), 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(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2205,plain,
% 1.33/1.52 ((~![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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2206,plain,
% 1.33/1.52 ((~![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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 1.33/1.52 tff(2207,plain,
% 1.33/1.52 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2206, 141, 2203, 997])).
% 1.33/1.52 tff(2208,plain,
% 1.33/1.52 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2207, 2202])).
% 1.33/1.52 tff(2209,plain,
% 1.33/1.52 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[501, 2208, 2193])).
% 1.33/1.52 tff(2210,plain,
% 1.33/1.52 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2209, 2200])).
% 1.33/1.52 tff(2211,plain,
% 1.33/1.52 (((~![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(s(elem!1)))))), z)) | (~r(s(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(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2212,plain,
% 1.33/1.52 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2213,plain,
% 1.33/1.52 (((~![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(s(elem!1)))))), s(z))) | (~r(s(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, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2212])).
% 1.33/1.52 tff(2214,plain,
% 1.33/1.52 (((~![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(s(elem!1)))))), s(z))) | (~r(s(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, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[2213, 2211])).
% 1.33/1.52 tff(2215,plain,
% 1.33/1.52 ((~![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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2216,plain,
% 1.33/1.52 ((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 1.33/1.52 tff(2217,plain,
% 1.33/1.52 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2216, 141, 1449, 2203])).
% 1.33/1.52 tff(2218,plain,
% 1.33/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2219,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(2220,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 1.33/1.52 tff(2221,plain,
% 1.33/1.52 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[2220, 32, 1554, 2217])).
% 1.33/1.52 tff(2222,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.33/1.52 tff(2223,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2224,plain,
% 1.33/1.52 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(2225,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[2224])).
% 1.33/1.52 tff(2226,plain,
% 1.33/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2225, 2223])).
% 1.33/1.53 tff(2227,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2228,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 1.33/1.53 tff(2229,plain,
% 1.33/1.53 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2228, 245, 2222, 919, 2221])).
% 1.33/1.53 tff(2230,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2229, 2210])).
% 1.33/1.53 tff(2231,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~(elem!1 = s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(2232,plain,
% 1.33/1.53 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2231, 2121, 2198, 2195, 2193, 2192, 2182])).
% 1.33/1.53 tff(2233,plain,
% 1.33/1.53 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[1820, 2232])).
% 1.33/1.53 tff(2234,plain,
% 1.33/1.53 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2130])).
% 1.33/1.53 tff(2235,plain,
% 1.33/1.53 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.33/1.53 inference(symmetry,[status(thm)],[2234])).
% 1.33/1.53 tff(2236,plain,
% 1.33/1.53 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2121])).
% 1.33/1.53 tff(2237,plain,
% 1.33/1.53 (b(s(elem!1), s(z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[308, 2236])).
% 1.33/1.53 tff(2238,plain,
% 1.33/1.53 (b(s(s(z)), s(z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2237, 2235])).
% 1.33/1.53 tff(2239,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2240,plain,
% 1.33/1.53 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2241,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2240])).
% 1.33/1.53 tff(2242,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2241, 2239])).
% 1.33/1.53 tff(2243,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2244,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2243, 2242])).
% 1.33/1.53 tff(2245,plain,
% 1.33/1.53 ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2244, 245, 2238, 2233])).
% 1.33/1.53 tff(2246,plain,
% 1.33/1.53 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2245, 2180, 2170])).
% 1.33/1.53 tff(2247,plain,
% 1.33/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2248,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2249,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 1.33/1.53 tff(2250,plain,
% 1.33/1.53 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2249, 32, 2246])).
% 1.33/1.53 tff(2251,plain,
% 1.33/1.53 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2250, 2165])).
% 1.33/1.53 tff(2252,plain,
% 1.33/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2253,plain,
% 1.33/1.53 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2254,plain,
% 1.33/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), 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(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2253])).
% 1.33/1.53 tff(2255,plain,
% 1.33/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), 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(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2254, 2252])).
% 1.33/1.53 tff(2256,plain,
% 1.33/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2257,plain,
% 1.33/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 1.33/1.53 tff(2258,plain,
% 1.33/1.53 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2257, 141, 2251])).
% 1.33/1.53 tff(2259,plain,
% 1.33/1.53 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2258, 2134])).
% 1.33/1.53 tff(2260,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2261,plain,
% 1.33/1.53 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2262,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2261])).
% 1.33/1.53 tff(2263,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2262, 2260])).
% 1.33/1.53 tff(2264,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2265,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 1.33/1.53 tff(2266,plain,
% 1.33/1.53 ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2265, 245, 2238, 2233])).
% 1.33/1.53 tff(2267,plain,
% 1.33/1.53 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2266, 2170])).
% 1.33/1.53 tff(2268,plain,
% 1.33/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2269,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2270,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 1.33/1.53 tff(2271,plain,
% 1.33/1.53 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2270, 32, 2267])).
% 1.33/1.53 tff(2272,plain,
% 1.33/1.53 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2271, 2259])).
% 1.33/1.53 tff(2273,plain,
% 1.33/1.53 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(z)))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2272])).
% 1.33/1.53 tff(2274,plain,
% 1.33/1.53 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.53 inference(symmetry,[status(thm)],[2273])).
% 1.33/1.53 tff(2275,plain,
% 1.33/1.53 (s(z) = s(s(s(s(s(s(z))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[591, 2274, 320, 2128])).
% 1.33/1.53 tff(2276,plain,
% 1.33/1.53 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2275])).
% 1.33/1.53 tff(2277,plain,
% 1.33/1.53 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.33/1.53 inference(symmetry,[status(thm)],[2276])).
% 1.33/1.53 tff(2278,plain,
% 1.33/1.53 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.33/1.53 inference(symmetry,[status(thm)],[2145])).
% 1.33/1.53 tff(2279,plain,
% 1.33/1.53 (s(s(s(s(s(z))))) = z),
% 1.33/1.53 inference(transitivity,[status(thm)],[2278, 2277, 52])).
% 1.33/1.53 tff(2280,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[734, 2279])).
% 1.33/1.53 tff(2281,plain,((~r(s(z), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(2282,plain,
% 1.33/1.53 (~r(s(z), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2281, 2093, 332, 1943, 1993, 2046, 2009, 289, 1, 2080, 2060, 131, 2034])).
% 1.33/1.53 tff(2283,plain,
% 1.33/1.53 (b(s(z), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[232, 2282])).
% 1.33/1.53 tff(2284,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2285,plain,
% 1.33/1.53 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2286,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2285])).
% 1.33/1.53 tff(2287,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2286, 2284])).
% 1.33/1.53 tff(2288,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2289,plain,
% 1.33/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2288, 2287])).
% 1.33/1.53 tff(2290,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2289, 245, 355, 655, 288, 2197, 1943])).
% 1.33/1.53 tff(2291,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(2292,plain,
% 1.33/1.53 (~b(s(z), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2291, 2283, 1993, 288, 1943])).
% 1.33/1.53 tff(2293,plain,
% 1.33/1.53 (r(s(z), s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[440, 2292, 9])).
% 1.33/1.53 tff(2294,plain,
% 1.33/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2295,plain,
% 1.33/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2296,plain,
% 1.33/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 1.33/1.53 tff(2297,plain,
% 1.33/1.53 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2296, 141, 2293, 2001])).
% 1.33/1.53 tff(2298,plain,
% 1.33/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(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(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2299,plain,
% 1.33/1.53 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2300,plain,
% 1.33/1.53 (((~![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(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2299])).
% 1.33/1.53 tff(2301,plain,
% 1.33/1.53 (((~![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(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[2300, 2298])).
% 1.33/1.53 tff(2302,plain,
% 1.33/1.53 ((~![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(z, s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(2303,plain,
% 1.33/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 1.33/1.53 tff(2304,plain,
% 1.33/1.53 (~r(z, s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[2303, 141, 2068, 2093])).
% 1.33/1.53 tff(2305,plain,
% 1.33/1.53 (b(z, s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[644, 2304])).
% 1.33/1.53 tff(2306,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2307,plain,
% 1.33/1.53 (((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(2308,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[2307])).
% 1.33/1.53 tff(2309,plain,
% 1.33/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2308, 2306])).
% 1.33/1.54 tff(2310,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2311,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.33/1.54 tff(2312,plain,
% 1.33/1.54 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2311, 245, 2283, 288, 2305, 1943])).
% 1.33/1.54 tff(2313,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[217, 2312, 2297])).
% 1.33/1.54 tff(2314,plain,((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (s(z) = s(elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(2315,plain,
% 1.33/1.54 (~b(s(elem!1), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2314, 1974, 1943, 1973, 1, 1971, 1958, 1972])).
% 1.33/1.54 tff(2316,plain,
% 1.33/1.54 (r(s(elem!1), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[653, 32, 638, 2315])).
% 1.33/1.54 tff(2317,plain,
% 1.33/1.54 (~r(elem!1, s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1082, 2316, 1971])).
% 1.33/1.54 tff(2318,plain,
% 1.33/1.54 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1086, 32, 2317])).
% 1.33/1.54 tff(2319,plain,
% 1.33/1.54 (b(elem!1, s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2318, 1962])).
% 1.33/1.54 tff(2320,plain,
% 1.33/1.54 (~r(s(elem!1), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[649, 2316, 1973])).
% 1.33/1.54 tff(2321,plain,
% 1.33/1.54 (b(s(elem!1), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[570, 2320, 105])).
% 1.33/1.54 tff(2322,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1257, 88, 1, 130])).
% 1.33/1.54 tff(2323,plain,
% 1.33/1.54 (~b(z, s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2066, 245, 1993, 2322, 1943])).
% 1.33/1.54 tff(2324,plain,
% 1.33/1.54 (~r(z, s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[187, 141, 289, 111])).
% 1.33/1.54 tff(2325,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[197, 2324, 2323])).
% 1.33/1.54 tff(2326,plain,(b(s(s(s(elem!1))), elem!1) | (~r(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(2327,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2326, 1973, 1943, 1, 1972])).
% 1.33/1.54 tff(2328,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2329,plain,
% 1.33/1.54 (((~b(s(elem!1), elem!1)) | (~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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2330,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2329])).
% 1.33/1.54 tff(2331,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2330, 2328])).
% 1.33/1.54 tff(2332,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2333,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2332, 2331])).
% 1.33/1.54 tff(2334,plain,
% 1.33/1.54 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2333, 245])).
% 1.33/1.54 tff(2335,plain,
% 1.33/1.54 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2334, 2327, 2321, 2319])).
% 1.33/1.54 tff(2336,plain,
% 1.33/1.54 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2091, 32, 2335])).
% 1.33/1.54 tff(2337,plain,
% 1.33/1.54 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2336, 1959])).
% 1.33/1.54 tff(2338,plain,
% 1.33/1.54 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1957, 399])).
% 1.33/1.54 tff(2339,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2326, 289, 1943, 1, 130])).
% 1.33/1.54 tff(2340,plain,
% 1.33/1.54 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2023, 245, 308, 2339, 1103])).
% 1.33/1.54 tff(2341,plain,
% 1.33/1.54 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[353, 2340, 2338])).
% 1.33/1.54 tff(2342,plain,
% 1.33/1.54 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2025, 305, 2338, 308, 1, 130])).
% 1.33/1.54 tff(2343,plain,
% 1.33/1.54 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[420, 2342, 7])).
% 1.33/1.54 tff(2344,plain,
% 1.33/1.54 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2338, 1941])).
% 1.33/1.54 tff(2345,plain,
% 1.33/1.54 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2334, 2339, 308, 1103])).
% 1.33/1.54 tff(2346,plain,
% 1.33/1.54 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2091, 32, 2345])).
% 1.33/1.54 tff(2347,plain,
% 1.33/1.54 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2346, 2344])).
% 1.33/1.54 tff(2348,plain,
% 1.33/1.54 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1252, 2338])).
% 1.33/1.54 tff(2349,plain,
% 1.33/1.54 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1239, 305, 2348])).
% 1.33/1.54 tff(2350,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2351,plain,
% 1.33/1.54 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2352,plain,
% 1.33/1.54 (((~![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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2351])).
% 1.33/1.54 tff(2353,plain,
% 1.33/1.54 (((~![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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2352, 2350])).
% 1.33/1.54 tff(2354,plain,
% 1.33/1.54 ((~![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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2355,plain,
% 1.33/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 1.33/1.54 tff(2356,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2355, 141, 1366, 407, 2133])).
% 1.33/1.54 tff(2357,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(2358,plain,
% 1.33/1.54 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2357, 2349, 2347])).
% 1.33/1.54 tff(2359,plain,
% 1.33/1.54 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1263, 2358, 1])).
% 1.33/1.54 tff(2360,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2361,plain,
% 1.33/1.54 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2362,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2361])).
% 1.33/1.54 tff(2363,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2362, 2360])).
% 1.33/1.54 tff(2364,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2365,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 1.33/1.54 tff(2366,plain,
% 1.33/1.54 (~b(z, s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2365, 245, 1993, 2359, 2343])).
% 1.33/1.54 tff(2367,plain,
% 1.33/1.54 (r(z, s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[644, 2366])).
% 1.33/1.54 tff(2368,plain,
% 1.33/1.54 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[415, 407, 371])).
% 1.33/1.54 tff(2369,plain,
% 1.33/1.54 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[420, 2368, 7])).
% 1.33/1.54 tff(2370,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(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(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2371,plain,
% 1.33/1.54 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2372,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2371])).
% 1.33/1.54 tff(2373,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2372, 2370])).
% 1.33/1.54 tff(2374,plain,
% 1.33/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2375,plain,
% 1.33/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.33/1.54 tff(2376,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2375, 141, 371, 1366, 407])).
% 1.33/1.54 tff(2377,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(2378,plain,
% 1.33/1.54 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2377, 407, 371])).
% 1.33/1.54 tff(2379,plain,
% 1.33/1.54 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1263, 2378, 1])).
% 1.33/1.54 tff(2380,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2381,plain,
% 1.33/1.54 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2382,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2381])).
% 1.33/1.54 tff(2383,plain,
% 1.33/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.33/1.54 tff(2384,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2385,plain,
% 1.33/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.33/1.54 tff(2386,plain,
% 1.33/1.54 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2385, 245, 1103, 2379, 2369])).
% 1.33/1.54 tff(2387,plain,
% 1.33/1.54 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1432, 2386, 399])).
% 1.33/1.54 tff(2388,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2389,plain,
% 1.33/1.54 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2390,plain,
% 1.33/1.54 (((~![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(elem!1, s(s(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2389])).
% 1.33/1.54 tff(2391,plain,
% 1.33/1.54 (((~![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(elem!1, s(s(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2390, 2388])).
% 1.33/1.54 tff(2392,plain,
% 1.33/1.54 ((~![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(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2393,plain,
% 1.33/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 1.33/1.54 tff(2394,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2393, 141, 2387, 2070, 407])).
% 1.33/1.54 tff(2395,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(2396,plain,
% 1.33/1.54 (~r(elem!1, s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2395, 2349, 399, 1103, 2341, 1])).
% 1.33/1.54 tff(2397,plain,
% 1.33/1.54 (b(elem!1, s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1724, 2396, 1673])).
% 1.33/1.54 tff(2398,plain,
% 1.33/1.54 (((~![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(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(z), s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2399,plain,
% 1.33/1.54 (((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(2400,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[2399])).
% 1.33/1.54 tff(2401,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(elem!1))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[2400, 2398])).
% 1.33/1.54 tff(2402,plain,
% 1.33/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(2403,plain,
% 1.33/1.54 ((~![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(z), s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2402, 2401])).
% 1.33/1.54 tff(2404,plain,
% 1.33/1.54 (~r(z, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[2403, 141, 1342, 486])).
% 1.33/1.54 tff(2405,plain,
% 1.33/1.54 (b(z, s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[1421, 2404])).
% 1.33/1.54 tff(2406,plain,
% 1.33/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(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(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2407,plain,
% 1.33/1.55 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2408,plain,
% 1.33/1.55 (((~![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(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2407])).
% 1.33/1.55 tff(2409,plain,
% 1.33/1.55 (((~![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(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2408, 2406])).
% 1.33/1.55 tff(2410,plain,
% 1.33/1.55 ((~![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(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2411,plain,
% 1.33/1.55 ((~![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(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 1.33/1.55 tff(2412,plain,
% 1.33/1.55 (~r(s(z), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2411, 141, 371, 486])).
% 1.33/1.55 tff(2413,plain,
% 1.33/1.55 (b(s(z), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1133, 2412])).
% 1.33/1.55 tff(2414,plain,
% 1.33/1.55 (((~![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(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))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2415,plain,
% 1.33/1.55 ((~![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(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2416,plain,
% 1.33/1.55 ((~![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(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 1.33/1.55 tff(2417,plain,
% 1.33/1.55 (~r(z, s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2416, 141, 371, 1342])).
% 1.33/1.55 tff(2418,plain,
% 1.33/1.55 (b(z, s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[197, 2417])).
% 1.33/1.55 tff(2419,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2420,plain,
% 1.33/1.55 (((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2421,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2420])).
% 1.33/1.55 tff(2422,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2421, 2419])).
% 1.33/1.55 tff(2423,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2424,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 1.33/1.55 tff(2425,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2424, 245, 1427, 2418, 2413, 2101, 2405])).
% 1.33/1.55 tff(2426,plain,((~r(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(2427,plain,
% 1.33/1.55 (~r(s(z), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2426, 2397, 2339, 2367, 2341])).
% 1.33/1.55 tff(2428,plain,
% 1.33/1.55 (b(s(z), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[440, 2427, 9])).
% 1.33/1.55 tff(2429,plain,
% 1.33/1.55 (((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2430,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), elem!1))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2429])).
% 1.33/1.55 tff(2431,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2430, 430])).
% 1.33/1.55 tff(2432,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2433,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), elem!1))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 1.33/1.55 tff(2434,plain,
% 1.33/1.55 (~b(s(z), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2433, 245, 308, 1103, 2428])).
% 1.33/1.55 tff(2435,plain,
% 1.33/1.55 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.33/1.55 inference(commutativity,[status(thm)],[])).
% 1.33/1.55 tff(2436,plain,
% 1.33/1.55 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(symmetry,[status(thm)],[2435])).
% 1.33/1.55 tff(2437,plain,
% 1.33/1.55 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2436])).
% 1.33/1.55 tff(2438,plain,
% 1.33/1.55 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[209, 2437])).
% 1.33/1.55 tff(2439,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(z), 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(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2440,plain,
% 1.33/1.55 (((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2441,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), 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(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2440])).
% 1.33/1.55 tff(2442,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), 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(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2441, 2439])).
% 1.33/1.55 tff(2443,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2444,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 1.33/1.55 tff(2445,plain,
% 1.33/1.55 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2444, 245, 308, 1103, 2428, 2343])).
% 1.33/1.55 tff(2446,plain,
% 1.33/1.55 (((~![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))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2447,plain,
% 1.33/1.55 ((~![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))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2448,plain,
% 1.33/1.55 ((~![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)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 1.33/1.55 tff(2449,plain,
% 1.33/1.55 ((s(z) = s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2448, 32, 2445])).
% 1.33/1.55 tff(2450,plain,
% 1.33/1.55 (r(s(z), s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2449, 2438])).
% 1.33/1.55 tff(2451,plain,
% 1.33/1.55 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1830, 245, 308, 1103, 2343])).
% 1.33/1.55 tff(2452,plain,
% 1.33/1.55 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1432, 2451, 399])).
% 1.33/1.55 tff(2453,plain,
% 1.33/1.55 (((~![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(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2454,plain,
% 1.33/1.55 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2455,plain,
% 1.33/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2454])).
% 1.33/1.55 tff(2456,plain,
% 1.33/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2455, 2453])).
% 1.33/1.55 tff(2457,plain,
% 1.33/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2458,plain,
% 1.33/1.55 ((~![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(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 1.33/1.55 tff(2459,plain,
% 1.33/1.55 (~r(s(z), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2458, 141, 2452, 2450])).
% 1.33/1.55 tff(2460,plain,
% 1.33/1.55 (s(z) = elem!1),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[389, 2459, 2434])).
% 1.33/1.55 tff(2461,plain,
% 1.33/1.55 (s(s(z)) = s(elem!1)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2460])).
% 1.33/1.55 tff(2462,plain,
% 1.33/1.55 (s(s(s(z))) = s(s(elem!1))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2461])).
% 1.33/1.55 tff(2463,plain,
% 1.33/1.55 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2462])).
% 1.33/1.55 tff(2464,plain,
% 1.33/1.55 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.55 inference(symmetry,[status(thm)],[2463])).
% 1.33/1.55 tff(2465,plain,
% 1.33/1.55 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2464])).
% 1.33/1.55 tff(2466,plain,
% 1.33/1.55 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2465, 2135])).
% 1.33/1.55 tff(2467,plain,
% 1.33/1.55 ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.33/1.55 inference(symmetry,[status(thm)],[2466])).
% 1.33/1.55 tff(2468,plain,
% 1.33/1.55 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2467])).
% 1.33/1.55 tff(2469,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2470,plain,
% 1.33/1.55 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2471,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(elem!1, s(z)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2470])).
% 1.33/1.55 tff(2472,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2471, 2469])).
% 1.33/1.55 tff(2473,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2474,plain,
% 1.33/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(elem!1, s(z)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.33/1.55 tff(2475,plain,
% 1.33/1.55 (~b(elem!1, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2474, 245, 308, 1103, 2428])).
% 1.33/1.55 tff(2476,plain,
% 1.33/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2477,plain,
% 1.33/1.55 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2478,plain,
% 1.33/1.55 (((~![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(elem!1, s(s(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(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2477])).
% 1.33/1.55 tff(2479,plain,
% 1.33/1.55 (((~![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(elem!1, s(s(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(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2478, 2476])).
% 1.33/1.55 tff(2480,plain,
% 1.33/1.55 ((~![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(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(2481,plain,
% 1.33/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 1.33/1.55 tff(2482,plain,
% 1.33/1.55 (~r(elem!1, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2481, 141, 2452, 2450])).
% 1.33/1.55 tff(2483,plain,
% 1.33/1.55 (elem!1 = s(z)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[281, 2482, 2475])).
% 1.33/1.55 tff(2484,plain,
% 1.33/1.55 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2156, 2483, 1])).
% 1.33/1.55 tff(2485,plain,
% 1.33/1.55 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2163, 2484])).
% 1.33/1.55 tff(2486,plain,
% 1.33/1.55 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2485, 2468])).
% 1.33/1.55 tff(2487,plain,
% 1.33/1.55 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2460])).
% 1.33/1.55 tff(2488,plain,
% 1.33/1.55 (r(z, s(z)) <=> r(z, elem!1)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2460])).
% 1.33/1.55 tff(2489,plain,
% 1.33/1.55 (r(z, elem!1) <=> r(z, s(z))),
% 1.33/1.55 inference(symmetry,[status(thm)],[2488])).
% 1.33/1.55 tff(2490,plain,
% 1.33/1.55 (r(z, s(z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[289, 2489])).
% 1.33/1.55 tff(2491,plain,
% 1.33/1.55 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2460])).
% 1.33/1.55 tff(2492,plain,
% 1.33/1.55 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.55 inference(symmetry,[status(thm)],[2491])).
% 1.33/1.55 tff(2493,plain,
% 1.33/1.55 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2463])).
% 1.33/1.55 tff(2494,plain,
% 1.33/1.55 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2493])).
% 1.33/1.55 tff(2495,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.55 inference(symmetry,[status(thm)],[2494])).
% 1.33/1.55 tff(2496,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.55 inference(transitivity,[status(thm)],[2495, 2492])).
% 1.33/1.55 tff(2497,plain,
% 1.33/1.55 (r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[130, 2496])).
% 1.33/1.55 tff(2498,plain,
% 1.33/1.55 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[331, 2338])).
% 1.33/1.55 tff(2499,plain,
% 1.33/1.55 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2493])).
% 1.33/1.55 tff(2500,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.33/1.55 inference(symmetry,[status(thm)],[2499])).
% 1.33/1.55 tff(2501,plain,
% 1.33/1.55 (b(s(s(s(s(s(z))))), z)),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[1943, 2500])).
% 1.33/1.55 tff(2502,plain,
% 1.33/1.55 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2493])).
% 1.33/1.55 tff(2503,plain,
% 1.33/1.55 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.33/1.55 inference(symmetry,[status(thm)],[2502])).
% 1.33/1.55 tff(2504,plain,
% 1.33/1.55 (b(z, s(s(s(s(s(z))))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[1993, 2503])).
% 1.33/1.55 tff(2505,plain,
% 1.33/1.55 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[2231, 2504, 2483, 2501, 2498, 2497, 2490])).
% 1.33/1.55 tff(2506,plain,
% 1.33/1.55 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1820, 2505])).
% 1.33/1.55 tff(2507,plain,
% 1.33/1.55 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[2506, 2487])).
% 1.33/1.55 tff(2508,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2509,plain,
% 1.33/1.55 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(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(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(2510,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[2509])).
% 1.33/1.55 tff(2511,plain,
% 1.33/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2510, 2508])).
% 1.33/1.56 tff(2512,plain,
% 1.33/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2513,plain,
% 1.33/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 1.33/1.56 tff(2514,plain,
% 1.33/1.56 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2513, 245, 308, 2339, 1103, 2507])).
% 1.33/1.56 tff(2515,plain,
% 1.33/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2516,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2517,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 1.33/1.56 tff(2518,plain,
% 1.33/1.56 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2517, 32, 2514])).
% 1.33/1.56 tff(2519,plain,
% 1.33/1.56 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2518, 2486])).
% 1.33/1.56 tff(2520,plain,
% 1.33/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(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(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2521,plain,
% 1.33/1.56 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2522,plain,
% 1.33/1.56 (((~![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(elem!1)))))), s(s(s(elem!1))))) | (~r(s(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(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2521])).
% 1.33/1.56 tff(2523,plain,
% 1.33/1.56 (((~![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(elem!1)))))), s(s(s(elem!1))))) | (~r(s(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(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2522, 2520])).
% 1.33/1.56 tff(2524,plain,
% 1.33/1.56 ((~![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(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2525,plain,
% 1.33/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.33/1.56 tff(2526,plain,
% 1.33/1.56 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2525, 141, 2347, 2519])).
% 1.33/1.56 tff(2527,plain,
% 1.33/1.56 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1775, 245, 308, 1103, 2507])).
% 1.33/1.56 tff(2528,plain,
% 1.33/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(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(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2529,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2530,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 1.33/1.56 tff(2531,plain,
% 1.33/1.56 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2530, 32, 2527])).
% 1.33/1.56 tff(2532,plain,
% 1.33/1.56 (s(s(s(s(s(s(elem!1)))))) = s(elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2531, 2526])).
% 1.33/1.56 tff(2533,plain,
% 1.33/1.56 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2532])).
% 1.33/1.56 tff(2534,plain,
% 1.33/1.56 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[2533])).
% 1.33/1.56 tff(2535,plain,
% 1.33/1.56 (s(z) = s(s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2460, 684, 2534, 320])).
% 1.33/1.56 tff(2536,plain,
% 1.33/1.56 (inj_0(s(z)) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2535])).
% 1.33/1.56 tff(2537,plain,
% 1.33/1.56 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 1.33/1.56 inference(symmetry,[status(thm)],[2536])).
% 1.33/1.56 tff(2538,plain,
% 1.33/1.56 (s(s(s(s(elem!1)))) = z),
% 1.33/1.56 inference(transitivity,[status(thm)],[1485, 2537, 52])).
% 1.33/1.56 tff(2539,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[66, 2538])).
% 1.33/1.56 tff(2540,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2541,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2540, 2321, 2319, 1943, 1972, 1973, 1, 1974, 1951])).
% 1.33/1.56 tff(2542,plain,
% 1.33/1.56 (~r(z, s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1982, 1973, 1972])).
% 1.33/1.56 tff(2543,plain,
% 1.33/1.56 (b(z, s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1992, 2542])).
% 1.33/1.56 tff(2544,plain,
% 1.33/1.56 (~b(z, s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2066, 245, 2543, 2541, 1943])).
% 1.33/1.56 tff(2545,plain,
% 1.33/1.56 (r(z, s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[197, 2544])).
% 1.33/1.56 tff(2546,plain,
% 1.33/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(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), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2547,plain,
% 1.33/1.56 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2548,plain,
% 1.33/1.56 (((~![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(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2547])).
% 1.33/1.56 tff(2549,plain,
% 1.33/1.56 (((~![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(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2548, 2546])).
% 1.33/1.56 tff(2550,plain,
% 1.33/1.56 ((~![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)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2551,plain,
% 1.33/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 1.33/1.56 tff(2552,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2551, 141, 2316, 2545, 2337])).
% 1.33/1.56 tff(2553,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~b(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2554,plain,
% 1.33/1.56 (~b(s(s(s(s(elem!1)))), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2553, 8, 1, 89, 90])).
% 1.33/1.56 tff(2555,plain,
% 1.33/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2556,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2557,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.33/1.56 tff(2558,plain,
% 1.33/1.56 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2557, 32, 66])).
% 1.33/1.56 tff(2559,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2558, 2554, 1938])).
% 1.33/1.56 tff(2560,plain,(b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(elem!1, z) | b(z, elem!1) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2561,plain,
% 1.33/1.56 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2560, 87, 84, 80, 1])).
% 1.33/1.56 tff(2562,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.33/1.56 tff(2563,plain,
% 1.33/1.56 (~(elem!1 = s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1074, 105])).
% 1.33/1.56 tff(2564,plain,
% 1.33/1.56 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.33/1.56 inference(symmetry,[status(thm)],[61])).
% 1.33/1.56 tff(2565,plain,
% 1.33/1.56 (s(s(s(s(elem!1)))) = elem!1),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[422, 2564])).
% 1.33/1.56 tff(2566,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2562, 2565])).
% 1.33/1.56 tff(2567,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2568,plain,
% 1.33/1.56 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2567, 2562])).
% 1.33/1.56 tff(2569,plain,
% 1.33/1.56 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1957, 2568])).
% 1.33/1.56 tff(2570,plain,
% 1.33/1.56 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[151, 8, 2562])).
% 1.33/1.56 tff(2571,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1297, 2322, 111, 11, 130, 564, 1])).
% 1.33/1.56 tff(2572,plain,(b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | b(s(elem!1), elem!1) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2573,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2572, 2570, 2569, 564, 1])).
% 1.33/1.56 tff(2574,plain,
% 1.33/1.56 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1274, 2570, 1, 564])).
% 1.33/1.56 tff(2575,plain,
% 1.33/1.56 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1274, 130, 1, 564])).
% 1.33/1.56 tff(2576,plain,
% 1.33/1.56 (~r(s(elem!1), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[649, 289, 572])).
% 1.33/1.56 tff(2577,plain,
% 1.33/1.56 (b(s(elem!1), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[653, 32, 638, 2576])).
% 1.33/1.56 tff(2578,plain,
% 1.33/1.56 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2579,plain,
% 1.33/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2578])).
% 1.33/1.56 tff(2580,plain,
% 1.33/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2579, 2002])).
% 1.33/1.56 tff(2581,plain,
% 1.33/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2582,plain,
% 1.33/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2581, 2580])).
% 1.33/1.56 tff(2583,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2582, 245, 2577, 1993, 556, 1943])).
% 1.33/1.56 tff(2584,plain,((~r(z, elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2585,plain,
% 1.33/1.56 (~b(s(s(s(s(elem!1)))), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2584, 2575, 1277, 289, 130])).
% 1.33/1.56 tff(2586,plain,
% 1.33/1.56 (r(s(s(s(s(elem!1)))), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2558, 2585])).
% 1.33/1.56 tff(2587,plain,
% 1.33/1.56 (((~![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)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2588,plain,
% 1.33/1.56 ((~![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)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2589,plain,
% 1.33/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2588, 2587])).
% 1.33/1.56 tff(2590,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2589, 141, 289, 130, 2586])).
% 1.33/1.56 tff(2591,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2592,plain,
% 1.33/1.56 (~r(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2591, 2570, 1, 564])).
% 1.33/1.56 tff(2593,plain,
% 1.33/1.56 (z = elem!1),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[175, 2592, 90])).
% 1.33/1.56 tff(2594,plain,
% 1.33/1.56 (s(z) = s(elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[117, 2593])).
% 1.33/1.56 tff(2595,plain,
% 1.33/1.56 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2594])).
% 1.33/1.56 tff(2596,plain,
% 1.33/1.56 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2594])).
% 1.33/1.56 tff(2597,plain,
% 1.33/1.56 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[2596])).
% 1.33/1.56 tff(2598,plain,
% 1.33/1.56 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2597])).
% 1.33/1.56 tff(2599,plain,
% 1.33/1.56 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1284, 2570, 1277])).
% 1.33/1.56 tff(2600,plain,
% 1.33/1.56 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[420, 2599, 7])).
% 1.33/1.56 tff(2601,plain,
% 1.33/1.56 (s(s(z)) = s(s(elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2594])).
% 1.33/1.56 tff(2602,plain,
% 1.33/1.56 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2601])).
% 1.33/1.56 tff(2603,plain,
% 1.33/1.56 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2602])).
% 1.33/1.56 tff(2604,plain,
% 1.33/1.56 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2603])).
% 1.33/1.56 tff(2605,plain,
% 1.33/1.56 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[2604])).
% 1.33/1.56 tff(2606,plain,
% 1.33/1.56 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2605])).
% 1.33/1.56 tff(2607,plain,
% 1.33/1.56 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.33/1.56 inference(symmetry,[status(thm)],[2606])).
% 1.33/1.56 tff(2608,plain,
% 1.33/1.56 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2593])).
% 1.33/1.56 tff(2609,plain,
% 1.33/1.56 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2608, 770])).
% 1.33/1.56 tff(2610,plain,
% 1.33/1.56 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.33/1.56 inference(transitivity,[status(thm)],[2609, 1470])).
% 1.33/1.56 tff(2611,plain,
% 1.33/1.56 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2610])).
% 1.33/1.56 tff(2612,plain,
% 1.33/1.56 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[734, 2611])).
% 1.33/1.56 tff(2613,plain,
% 1.33/1.56 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2594])).
% 1.33/1.56 tff(2614,plain,
% 1.33/1.56 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.33/1.56 inference(symmetry,[status(thm)],[2613])).
% 1.33/1.56 tff(2615,plain,
% 1.33/1.56 (r(s(z), elem!1)),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[1277, 2614])).
% 1.33/1.56 tff(2616,plain,
% 1.33/1.56 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2594])).
% 1.33/1.56 tff(2617,plain,
% 1.33/1.56 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.56 inference(symmetry,[status(thm)],[2616])).
% 1.33/1.56 tff(2618,plain,
% 1.33/1.56 (b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2600, 2617])).
% 1.33/1.56 tff(2619,plain,
% 1.33/1.56 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[39])).
% 1.33/1.56 tff(2620,plain,
% 1.33/1.56 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 1.33/1.56 inference(symmetry,[status(thm)],[2619])).
% 1.33/1.56 tff(2621,plain,
% 1.33/1.56 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[1494])).
% 1.33/1.56 tff(2622,plain,
% 1.33/1.56 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[39])).
% 1.33/1.56 tff(2623,plain,
% 1.33/1.56 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2622, 2621, 2620])).
% 1.33/1.56 tff(2624,plain,
% 1.33/1.56 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.56 inference(symmetry,[status(thm)],[1575])).
% 1.33/1.56 tff(2625,plain,
% 1.33/1.56 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.56 inference(transitivity,[status(thm)],[1573, 2624])).
% 1.33/1.56 tff(2626,plain,
% 1.33/1.56 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2625])).
% 1.33/1.56 tff(2627,plain,
% 1.33/1.56 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[1494])).
% 1.33/1.56 tff(2628,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.33/1.56 tff(2629,plain,
% 1.33/1.56 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 1.33/1.56 tff(2630,plain,
% 1.33/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(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))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2631,plain,
% 1.33/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2632,plain,
% 1.33/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 1.33/1.56 tff(2633,plain,
% 1.33/1.56 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2632, 141, 572, 2629])).
% 1.33/1.56 tff(2634,plain,
% 1.33/1.56 (~r(s(s(s(s(s(z))))), s(z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2633, 2626])).
% 1.33/1.56 tff(2635,plain,
% 1.33/1.56 (b(s(s(s(s(s(z))))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[809, 2634])).
% 1.33/1.56 tff(2636,plain,
% 1.33/1.56 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2635, 2623])).
% 1.33/1.56 tff(2637,plain,
% 1.33/1.56 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[39, 1495])).
% 1.33/1.56 tff(2638,plain,
% 1.33/1.56 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[2637])).
% 1.33/1.56 tff(2639,plain,
% 1.33/1.56 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[39])).
% 1.33/1.56 tff(2640,plain,
% 1.33/1.56 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2639, 2638])).
% 1.33/1.56 tff(2641,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.33/1.56 tff(2642,plain,
% 1.33/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(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), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2643,plain,
% 1.33/1.56 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2644,plain,
% 1.33/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[2643])).
% 1.33/1.56 tff(2645,plain,
% 1.33/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[2644, 2642])).
% 1.33/1.56 tff(2646,plain,
% 1.33/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(2647,plain,
% 1.33/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.33/1.56 tff(2648,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2647, 141, 619, 2641, 2628])).
% 1.33/1.56 tff(2649,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(2650,plain,
% 1.33/1.56 (~r(s(z), s(s(s(s(s(z))))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[2649, 2628, 619])).
% 1.33/1.56 tff(2651,plain,
% 1.33/1.56 (b(s(z), s(s(s(s(s(z))))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1698, 2650])).
% 1.33/1.56 tff(2652,plain,
% 1.33/1.56 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[2651, 2640])).
% 1.33/1.56 tff(2653,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.33/1.56 tff(2654,plain,
% 1.33/1.56 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1520, 141, 130, 2629])).
% 1.33/1.56 tff(2655,plain,
% 1.33/1.56 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[1526, 32, 1523, 2654])).
% 1.33/1.56 tff(2656,assumption,(b(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.33/1.56 tff(2657,assumption,(b(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.33/1.56 tff(2658,plain,
% 1.33/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(2659,plain,
% 1.33/1.56 (((~b(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)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2660,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2659])).
% 1.33/1.57 tff(2661,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[2660, 2658])).
% 1.33/1.57 tff(2662,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2663,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2662, 2661])).
% 1.33/1.57 tff(2664,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2663, 245, 1596, 2657, 2656, 2653])).
% 1.33/1.57 tff(2665,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(2666,plain,
% 1.33/1.57 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2665, 2655, 2653, 2652])).
% 1.33/1.57 tff(2667,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2666, 2636])).
% 1.33/1.57 tff(2668,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(2669,plain,
% 1.33/1.57 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2668, 2618, 2594, 1490, 2570, 1277, 2615])).
% 1.33/1.57 tff(2670,plain,
% 1.33/1.57 (b(s(s(s(s(s(z))))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[787, 2669, 2612])).
% 1.33/1.57 tff(2671,plain,
% 1.33/1.57 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2670, 2607])).
% 1.33/1.57 tff(2672,plain,
% 1.33/1.57 (~b(s(s(s(s(elem!1)))), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1968, 2593, 8])).
% 1.33/1.57 tff(2673,plain,
% 1.33/1.57 (r(s(s(s(s(elem!1)))), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2558, 2672])).
% 1.33/1.57 tff(2674,plain,
% 1.33/1.57 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2593])).
% 1.33/1.57 tff(2675,plain,
% 1.33/1.57 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.33/1.57 inference(symmetry,[status(thm)],[2674])).
% 1.33/1.57 tff(2676,plain,
% 1.33/1.57 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2675])).
% 1.33/1.57 tff(2677,plain,
% 1.33/1.57 (~b(elem!1, z)),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[79, 2676])).
% 1.33/1.57 tff(2678,plain,
% 1.33/1.57 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1937, 2677, 90, 8, 2673, 1])).
% 1.33/1.57 tff(2679,plain,
% 1.33/1.57 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(commutativity,[status(thm)],[])).
% 1.33/1.57 tff(2680,plain,
% 1.33/1.57 ((~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2679])).
% 1.33/1.57 tff(2681,plain,
% 1.33/1.57 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(commutativity,[status(thm)],[])).
% 1.33/1.57 tff(2682,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.33/1.57 tff(2683,plain,
% 1.33/1.57 ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2682])).
% 1.33/1.57 tff(2684,plain,
% 1.33/1.57 ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[2683, 2681])).
% 1.33/1.57 tff(2685,plain,
% 1.33/1.57 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.33/1.57 inference(symmetry,[status(thm)],[2684])).
% 1.33/1.57 tff(2686,plain,
% 1.33/1.57 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2682])).
% 1.33/1.57 tff(2687,plain,
% 1.33/1.57 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[1485, 2686, 320, 2682])).
% 1.33/1.57 tff(2688,plain,
% 1.33/1.57 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2687, 2685])).
% 1.33/1.57 tff(2689,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1523, 2688])).
% 1.33/1.57 tff(2690,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(2691,plain,
% 1.33/1.57 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2690, 1490])).
% 1.33/1.57 tff(2692,plain,
% 1.33/1.57 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2691, 2680])).
% 1.33/1.57 tff(2693,plain,
% 1.33/1.57 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1571, 2594, 1])).
% 1.33/1.57 tff(2694,plain,
% 1.33/1.57 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2593])).
% 1.33/1.57 tff(2695,plain,
% 1.33/1.57 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[2694, 1547])).
% 1.33/1.57 tff(2696,plain,
% 1.33/1.57 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.33/1.57 inference(transitivity,[status(thm)],[2695, 1548])).
% 1.33/1.57 tff(2697,plain,
% 1.33/1.57 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2696])).
% 1.33/1.57 tff(2698,plain,
% 1.33/1.57 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[1554, 2697])).
% 1.33/1.57 tff(2699,plain,
% 1.33/1.57 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[331, 2569])).
% 1.33/1.57 tff(2700,assumption,(r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.33/1.57 tff(2701,plain,
% 1.33/1.57 (((~![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(elem!1)))))), elem!1)) | (~r(s(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(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2702,plain,
% 1.33/1.57 ((~![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(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2703,plain,
% 1.33/1.57 ((~![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(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.33/1.57 tff(2704,plain,
% 1.33/1.57 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2703, 141, 130, 2700])).
% 1.33/1.57 tff(2705,plain,
% 1.33/1.57 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[501, 2704, 2193])).
% 1.33/1.57 tff(2706,plain,
% 1.33/1.57 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1900, 245, 556, 10, 2705])).
% 1.33/1.57 tff(2707,plain,
% 1.33/1.57 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2706, 1546])).
% 1.33/1.57 tff(2708,plain,
% 1.33/1.57 (((~![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(elem!1)))))), elem!1)) | (~r(s(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(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2709,plain,
% 1.33/1.57 ((~![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(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2710,plain,
% 1.33/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 1.33/1.57 tff(2711,plain,
% 1.33/1.57 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2710, 141, 572, 2700])).
% 1.33/1.57 tff(2712,plain,
% 1.33/1.57 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2711, 1780])).
% 1.33/1.57 tff(2713,plain,
% 1.33/1.57 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1820, 2712])).
% 1.33/1.57 tff(2714,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2713, 2707])).
% 1.33/1.57 tff(2715,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(2716,plain,
% 1.33/1.57 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2715, 2594, 2574, 2600, 2699, 2570, 1277])).
% 1.33/1.57 tff(2717,plain,
% 1.33/1.57 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1768, 2716, 2698])).
% 1.33/1.57 tff(2718,assumption,(b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.33/1.57 tff(2719,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2720,plain,
% 1.33/1.57 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(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(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2721,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2720])).
% 1.33/1.57 tff(2722,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[2721, 2719])).
% 1.33/1.57 tff(2723,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2724,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 1.33/1.57 tff(2725,plain,
% 1.33/1.57 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2724, 245, 1427, 2101, 2718, 1543])).
% 1.33/1.57 tff(2726,plain,
% 1.33/1.57 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1607, 32, 1542, 2725])).
% 1.33/1.57 tff(2727,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(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(X0, 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))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2728,plain,
% 1.33/1.57 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(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))))), elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2729,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2728])).
% 1.33/1.57 tff(2730,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[2729, 2727])).
% 1.33/1.57 tff(2731,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2732,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.33/1.57 tff(2733,plain,
% 1.33/1.57 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2732, 245, 1427, 2101, 1543])).
% 1.33/1.57 tff(2734,plain,
% 1.33/1.57 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2733, 1610])).
% 1.33/1.57 tff(2735,plain,
% 1.33/1.57 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1515, 2734])).
% 1.33/1.57 tff(2736,plain,
% 1.33/1.57 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2735, 1609])).
% 1.33/1.57 tff(2737,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(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(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2738,plain,
% 1.33/1.57 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2739,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1)))))), elem!1)) | (~b(s(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(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2738])).
% 1.33/1.57 tff(2740,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1)))))), elem!1)) | (~b(s(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(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[2739, 2737])).
% 1.33/1.57 tff(2741,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2742,plain,
% 1.33/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 1.33/1.57 tff(2743,plain,
% 1.33/1.57 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2742, 245, 1427, 2101, 2718])).
% 1.33/1.57 tff(2744,plain,
% 1.33/1.57 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2743, 1618])).
% 1.33/1.57 tff(2745,plain,
% 1.33/1.57 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1630, 2744, 1616])).
% 1.33/1.57 tff(2746,plain,
% 1.33/1.57 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2745, 1615])).
% 1.33/1.57 tff(2747,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1638, 141, 2746, 2736, 2726])).
% 1.33/1.57 tff(2748,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(2749,plain,
% 1.33/1.57 (~b(elem!1, s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2748, 2717, 2693, 2692, 2678, 2594, 2671])).
% 1.33/1.57 tff(2750,plain,
% 1.33/1.57 (r(elem!1, s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1724, 2749, 1673])).
% 1.33/1.57 tff(2751,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.57 tff(2752,plain,
% 1.33/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2753,plain,
% 1.33/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2754,plain,
% 1.33/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 1.33/1.57 tff(2755,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2754, 141, 2070, 130, 2751])).
% 1.33/1.57 tff(2756,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(2757,plain,
% 1.33/1.57 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2756, 2070, 130])).
% 1.33/1.57 tff(2758,plain,
% 1.33/1.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[1320, 2757, 1487])).
% 1.33/1.57 tff(2759,plain,
% 1.33/1.57 (((~![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))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2760,plain,
% 1.33/1.57 ((~![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))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(2761,plain,
% 1.33/1.57 ((~![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)))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 1.33/1.57 tff(2762,plain,
% 1.33/1.57 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2761, 141])).
% 1.33/1.57 tff(2763,plain,
% 1.33/1.57 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[2762, 2070, 1367])).
% 1.33/1.57 tff(2764,plain,
% 1.33/1.57 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[353, 2763, 11])).
% 1.33/1.57 tff(2765,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2766,plain,
% 1.33/1.57 (((~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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(2767,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[2766])).
% 1.33/1.57 tff(2768,plain,
% 1.33/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2767, 2765])).
% 1.33/1.58 tff(2769,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2770,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 1.33/1.58 tff(2771,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2770, 245, 2764, 556, 2758, 10])).
% 1.33/1.58 tff(2772,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2773,plain,
% 1.33/1.58 (~r(elem!1, s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2772, 2750, 2600, 2569, 1312, 2574, 2570])).
% 1.33/1.58 tff(2774,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.33/1.58 tff(2775,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.33/1.58 tff(2776,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1086, 32, 2775, 426, 2774])).
% 1.33/1.58 tff(2777,plain,(r(elem!1, s(elem!1)) | b(elem!1, s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2778,plain,
% 1.33/1.58 (b(elem!1, s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2777, 2773, 2563])).
% 1.33/1.58 tff(2779,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2780,plain,
% 1.33/1.58 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2781,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2780])).
% 1.33/1.58 tff(2782,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2781, 2779])).
% 1.33/1.58 tff(2783,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2784,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 1.33/1.58 tff(2785,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2784, 245, 1287, 1427, 1103, 556, 10])).
% 1.33/1.58 tff(2786,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2787,plain,
% 1.33/1.58 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2786, 556, 1427, 1103, 1287])).
% 1.33/1.58 tff(2788,plain,
% 1.33/1.58 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[420, 2787, 164])).
% 1.33/1.58 tff(2789,plain,
% 1.33/1.58 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1284, 2788, 572])).
% 1.33/1.58 tff(2790,plain,
% 1.33/1.58 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[151, 2789, 2562])).
% 1.33/1.58 tff(2791,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2792,plain,
% 1.33/1.58 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2793,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2792])).
% 1.33/1.58 tff(2794,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2793, 2791])).
% 1.33/1.58 tff(2795,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2796,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 1.33/1.58 tff(2797,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2796, 245, 1287, 1427, 1103, 2790, 556])).
% 1.33/1.58 tff(2798,plain,((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2799,plain,
% 1.33/1.58 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2798, 2778, 2574, 7, 2562, 2678, 1277])).
% 1.33/1.58 tff(2800,plain,
% 1.33/1.58 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[353, 2799, 2569])).
% 1.33/1.58 tff(2801,plain,
% 1.33/1.58 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2395, 2800, 2568, 2750, 2778, 1])).
% 1.33/1.58 tff(2802,plain,
% 1.33/1.58 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1239, 2801, 1304])).
% 1.33/1.58 tff(2803,plain,
% 1.33/1.58 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2756, 2750, 2570])).
% 1.33/1.58 tff(2804,plain,
% 1.33/1.58 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1320, 2803, 1312])).
% 1.33/1.58 tff(2805,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2806,plain,
% 1.33/1.58 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2807,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2806])).
% 1.33/1.58 tff(2808,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2807, 2805])).
% 1.33/1.58 tff(2809,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2810,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2809, 2808])).
% 1.33/1.58 tff(2811,plain,
% 1.33/1.58 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2810, 245, 2574, 2804, 2802])).
% 1.33/1.58 tff(2812,plain,
% 1.33/1.58 (~b(s(z), s(s(s(elem!1))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2811, 2598])).
% 1.33/1.58 tff(2813,plain,
% 1.33/1.58 (r(s(z), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1133, 2812])).
% 1.33/1.58 tff(2814,plain,
% 1.33/1.58 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2813, 2595])).
% 1.33/1.58 tff(2815,plain,
% 1.33/1.58 (((~![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))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2816,plain,
% 1.33/1.58 (((~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))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2817,plain,
% 1.33/1.58 (((~![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)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2816])).
% 1.33/1.58 tff(2818,plain,
% 1.33/1.58 (((~![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))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.33/1.58 tff(2819,plain,
% 1.33/1.58 ((~![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)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2820,plain,
% 1.33/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.33/1.58 tff(2821,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2820, 141, 1277, 2750, 2814])).
% 1.33/1.58 tff(2822,plain,(b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | b(z, elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2823,plain,
% 1.33/1.58 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2822, 90, 2562, 1, 564])).
% 1.33/1.58 tff(2824,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.33/1.58 tff(2825,plain,
% 1.33/1.58 (~r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[670, 176, 572, 9])).
% 1.33/1.58 tff(2826,plain,
% 1.33/1.58 (~r(z, s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[632, 141, 176, 572])).
% 1.33/1.58 tff(2827,plain,
% 1.33/1.58 (b(z, s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[644, 2826])).
% 1.33/1.58 tff(2828,plain,
% 1.33/1.58 (~r(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[649, 176, 572])).
% 1.33/1.58 tff(2829,plain,
% 1.33/1.58 (b(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1039, 2828])).
% 1.33/1.58 tff(2830,plain,
% 1.33/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2831,plain,
% 1.33/1.58 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2832,plain,
% 1.33/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2831])).
% 1.33/1.58 tff(2833,plain,
% 1.33/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2832, 2830])).
% 1.33/1.58 tff(2834,plain,
% 1.33/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2835,plain,
% 1.33/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2834, 2833])).
% 1.33/1.58 tff(2836,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2835, 141, 1368, 572, 1366])).
% 1.33/1.58 tff(2837,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2838,plain,
% 1.33/1.58 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2837, 1366, 572])).
% 1.33/1.58 tff(2839,plain,
% 1.33/1.58 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1432, 2838, 2568])).
% 1.33/1.58 tff(2840,plain,
% 1.33/1.58 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2377, 371, 1366])).
% 1.33/1.58 tff(2841,plain,
% 1.33/1.58 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1239, 2840, 1309])).
% 1.33/1.58 tff(2842,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2843,plain,
% 1.33/1.58 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2844,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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(elem!1))), s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2843])).
% 1.33/1.58 tff(2845,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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(elem!1))), s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2844, 2842])).
% 1.33/1.58 tff(2846,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2847,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 1.33/1.58 tff(2848,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2847, 245, 1390, 1427, 2824, 1276])).
% 1.33/1.58 tff(2849,plain,((~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(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2850,plain,
% 1.33/1.58 (~b(s(s(s(elem!1))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2849, 2841, 1390, 2824])).
% 1.33/1.58 tff(2851,plain,
% 1.33/1.58 (r(s(s(s(elem!1))), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[110, 2850, 102])).
% 1.33/1.58 tff(2852,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[575, 141, 371, 572, 2851])).
% 1.33/1.58 tff(2853,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (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)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(2854,plain,
% 1.33/1.58 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2853, 2839, 96, 1366, 2824, 1304, 572])).
% 1.33/1.58 tff(2855,plain,
% 1.33/1.58 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[353, 2854, 2569])).
% 1.33/1.58 tff(2856,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, 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(X0, 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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2857,plain,
% 1.33/1.58 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(2858,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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(X0, 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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[2857])).
% 1.33/1.58 tff(2859,plain,
% 1.33/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(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(X0, 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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[2858, 2856])).
% 1.33/1.58 tff(2860,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(2861,plain,
% 1.33/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[2860, 2859])).
% 1.33/1.58 tff(2862,plain,
% 1.33/1.58 (~b(z, s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2861, 245, 2855, 2829, 2827])).
% 1.33/1.58 tff(2863,plain,
% 1.33/1.58 (r(z, s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[197, 2862])).
% 1.33/1.58 tff(2864,plain,
% 1.33/1.58 (~r(elem!1, s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[2078, 2863, 176])).
% 1.33/1.58 tff(2865,plain,
% 1.33/1.58 (b(elem!1, s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[1724, 2864, 1673])).
% 1.33/1.58 tff(2866,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2867,plain,
% 1.33/1.59 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2868,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2867])).
% 1.33/1.59 tff(2869,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[2868, 2866])).
% 1.33/1.59 tff(2870,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(2871,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 1.33/1.59 tff(2872,plain,
% 1.33/1.59 (~b(s(s(s(elem!1))), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2871, 245, 2855, 2829, 2827])).
% 1.33/1.59 tff(2873,plain,
% 1.33/1.59 (r(s(s(s(elem!1))), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[37, 2872])).
% 1.33/1.59 tff(2874,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[179, 141, 289, 1355, 170])).
% 1.33/1.59 tff(2875,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(2876,plain,
% 1.33/1.59 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2875, 176, 2873])).
% 1.33/1.59 tff(2877,plain,
% 1.33/1.59 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[110, 2876, 96])).
% 1.33/1.59 tff(2878,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2879,plain,
% 1.33/1.59 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2880,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2879])).
% 1.33/1.59 tff(2881,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[2880, 2878])).
% 1.33/1.59 tff(2882,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(2883,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2882, 2881])).
% 1.33/1.59 tff(2884,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2883, 245, 1287, 1427, 2101, 2824, 1276])).
% 1.33/1.59 tff(2885,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(2886,plain,
% 1.33/1.59 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2885, 2877, 2824, 2855, 2865])).
% 1.33/1.59 tff(2887,plain,
% 1.33/1.59 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1239, 2886, 1304])).
% 1.33/1.59 tff(2888,plain,
% 1.33/1.59 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2569, 1941])).
% 1.33/1.59 tff(2889,plain,
% 1.33/1.59 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2357, 1366, 2133])).
% 1.33/1.59 tff(2890,plain,
% 1.33/1.59 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1239, 2889, 1309])).
% 1.33/1.59 tff(2891,plain,
% 1.33/1.59 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2885, 2890, 1427, 2101, 1287])).
% 1.33/1.59 tff(2892,plain,
% 1.33/1.59 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[151, 2891, 2562])).
% 1.33/1.59 tff(2893,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1272, 141, 572, 2892, 1366])).
% 1.33/1.59 tff(2894,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(2895,plain,
% 1.33/1.59 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2894, 2877, 2562, 1366, 2855, 2865, 1304, 572])).
% 1.33/1.59 tff(2896,plain,
% 1.33/1.59 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2091, 32, 2895])).
% 1.33/1.59 tff(2897,plain,
% 1.33/1.59 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2896, 2888])).
% 1.33/1.59 tff(2898,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.33/1.59 tff(2899,plain,
% 1.33/1.59 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2898])).
% 1.33/1.59 tff(2900,plain,
% 1.33/1.59 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.33/1.59 inference(transitivity,[status(thm)],[2899, 1548])).
% 1.33/1.59 tff(2901,plain,
% 1.33/1.59 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2900])).
% 1.33/1.59 tff(2902,plain,
% 1.33/1.59 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[465, 2901])).
% 1.33/1.59 tff(2903,plain,
% 1.33/1.59 (elem!1 = s(z)),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2898, 338])).
% 1.33/1.59 tff(2904,plain,
% 1.33/1.59 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2156, 2903, 1])).
% 1.33/1.59 tff(2905,plain,
% 1.33/1.59 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2163, 2904])).
% 1.33/1.59 tff(2906,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.33/1.59 tff(2907,plain,
% 1.33/1.59 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.33/1.59 inference(symmetry,[status(thm)],[2906])).
% 1.33/1.59 tff(2908,plain,
% 1.33/1.59 (s(s(z)) = s(elem!1)),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2898])).
% 1.33/1.59 tff(2909,plain,
% 1.33/1.59 (s(s(s(z))) = s(s(elem!1))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2908])).
% 1.33/1.59 tff(2910,plain,
% 1.33/1.59 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2909])).
% 1.33/1.59 tff(2911,plain,
% 1.33/1.59 (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[2910, 2907])).
% 1.33/1.59 tff(2912,assumption,(~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.33/1.59 tff(2913,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2912, 2911])).
% 1.33/1.59 tff(2914,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(2915,plain,
% 1.33/1.59 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2914, 2905, 2898])).
% 1.33/1.59 tff(2916,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.59 tff(2917,plain,
% 1.33/1.59 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2517, 32, 2916, 2743])).
% 1.33/1.59 tff(2918,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2919,plain,
% 1.33/1.59 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2920,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2919])).
% 1.33/1.59 tff(2921,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[2920, 2918])).
% 1.33/1.59 tff(2922,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(2923,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2922, 2921])).
% 1.33/1.59 tff(2924,plain,
% 1.33/1.59 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2923, 245, 1427, 2101, 2824, 2718])).
% 1.33/1.59 tff(2925,plain,
% 1.33/1.59 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[501, 2924, 2193])).
% 1.33/1.59 tff(2926,plain,
% 1.33/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2927,plain,
% 1.33/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(2928,plain,
% 1.33/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2927, 2926])).
% 1.33/1.59 tff(2929,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2928, 141, 407, 2925, 2917])).
% 1.33/1.59 tff(2930,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(2931,plain,
% 1.33/1.59 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2930, 2915, 407, 2193, 1427, 2101, 2824])).
% 1.33/1.59 tff(2932,plain,
% 1.33/1.59 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1768, 2931, 2902])).
% 1.33/1.59 tff(2933,plain,
% 1.33/1.59 (((~![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(elem!1)))))), elem!1)) | (~r(s(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(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2934,plain,
% 1.33/1.59 ((~![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(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(2935,plain,
% 1.33/1.59 ((~![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(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 1.33/1.59 tff(2936,plain,
% 1.33/1.59 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2935, 141, 289, 2932])).
% 1.33/1.59 tff(2937,plain,
% 1.33/1.59 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2220, 32, 1554, 2936])).
% 1.33/1.59 tff(2938,plain,
% 1.33/1.59 (b(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[1039, 2576])).
% 1.33/1.59 tff(2939,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.59 tff(2940,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2941,plain,
% 1.33/1.59 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2942,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2941])).
% 1.33/1.59 tff(2943,plain,
% 1.33/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[2942, 2940])).
% 1.33/1.59 tff(2944,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(2945,plain,
% 1.33/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2944, 2943])).
% 1.33/1.59 tff(2946,plain,
% 1.33/1.59 (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2945, 245, 2939, 2938, 645, 2937])).
% 1.33/1.59 tff(2947,plain,
% 1.33/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(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(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2948,plain,
% 1.33/1.59 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(2949,plain,
% 1.33/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[2948])).
% 1.33/1.59 tff(2950,plain,
% 1.33/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[2949, 2947])).
% 1.33/1.59 tff(2951,plain,
% 1.33/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(2952,plain,
% 1.33/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[2951, 2950])).
% 1.33/1.59 tff(2953,plain,
% 1.33/1.59 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[2952, 141, 572, 2932])).
% 1.33/1.59 tff(2954,plain,
% 1.33/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(2955,plain,
% 1.33/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.60 inference(quant_inst,[status(thm)],[])).
% 1.33/1.60 tff(2956,plain,
% 1.33/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.60 inference(modus_ponens,[status(thm)],[2955, 2954])).
% 1.33/1.60 tff(2957,plain,
% 1.33/1.60 ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[2956, 32, 2953])).
% 1.33/1.60 tff(2958,plain,
% 1.33/1.60 (s(elem!1) = s(s(s(s(s(s(elem!1))))))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[2957, 2946])).
% 1.33/1.60 tff(2959,plain,
% 1.33/1.60 (s(s(s(s(s(s(elem!1)))))) = s(elem!1)),
% 1.33/1.60 inference(symmetry,[status(thm)],[2958])).
% 1.33/1.60 tff(2960,plain,
% 1.33/1.60 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(elem!1))),
% 1.33/1.60 inference(monotonicity,[status(thm)],[2959])).
% 1.33/1.60 tff(2961,plain,
% 1.33/1.60 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.60 inference(symmetry,[status(thm)],[2960])).
% 1.33/1.60 tff(2962,plain,
% 1.33/1.60 (s(z) = s(s(s(s(s(elem!1)))))),
% 1.33/1.60 inference(transitivity,[status(thm)],[2898, 684, 2961, 320])).
% 1.33/1.60 tff(2963,plain,
% 1.33/1.60 (inj_0(s(z)) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.33/1.60 inference(monotonicity,[status(thm)],[2962])).
% 1.33/1.60 tff(2964,plain,
% 1.33/1.60 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 1.33/1.60 inference(symmetry,[status(thm)],[2963])).
% 1.33/1.60 tff(2965,plain,
% 1.33/1.60 (s(s(s(s(elem!1)))) = z),
% 1.33/1.60 inference(transitivity,[status(thm)],[1485, 2964, 52])).
% 1.33/1.60 tff(2966,plain,
% 1.33/1.60 ($false),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[66, 2965])).
% 1.33/1.60 tff(2967,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.60 tff(2968,plain,
% 1.33/1.60 (~(s(z) = elem!1)),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[2967, 2897, 572, 176, 2887, 2699, 2877, 2865, 2824, 1])).
% 1.33/1.60 tff(2969,plain,
% 1.33/1.60 (b(s(z), elem!1)),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[389, 2968, 2825])).
% 1.33/1.60 tff(2970,plain,
% 1.33/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(2971,plain,
% 1.33/1.60 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(2972,plain,
% 1.33/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.33/1.60 inference(monotonicity,[status(thm)],[2971])).
% 1.33/1.60 tff(2973,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[2972, 2970])).
% 1.43/1.60 tff(2974,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(2975,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 1.43/1.60 tff(2976,plain,
% 1.43/1.60 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2975, 245, 2839, 2969, 2824])).
% 1.43/1.60 tff(2977,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[217, 2976])).
% 1.43/1.60 tff(2978,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(2979,plain,
% 1.43/1.60 (((~b(elem!1, s(s(s(s(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)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(2980,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(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)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[2979])).
% 1.43/1.60 tff(2981,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(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)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[2980, 2978])).
% 1.43/1.60 tff(2982,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(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)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(2983,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[2982, 2981])).
% 1.43/1.60 tff(2984,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2983, 245, 1390, 1427, 2101, 1528])).
% 1.43/1.60 tff(2985,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(2986,plain,
% 1.43/1.60 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2985, 2877, 2839, 2865])).
% 1.43/1.60 tff(2987,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1320, 2986, 1312])).
% 1.43/1.60 tff(2988,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(2989,plain,
% 1.43/1.60 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(2990,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[2989])).
% 1.43/1.60 tff(2991,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[2990, 2988])).
% 1.43/1.60 tff(2992,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(2993,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 1.43/1.60 tff(2994,plain,
% 1.43/1.60 (~b(s(z), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2993, 245, 2877, 2969, 2865])).
% 1.43/1.60 tff(2995,plain,
% 1.43/1.60 (r(s(z), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1133, 2994])).
% 1.43/1.60 tff(2996,plain,
% 1.43/1.60 (((~![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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(2997,plain,
% 1.43/1.60 (((~r(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(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(2998,plain,
% 1.43/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[2997])).
% 1.43/1.60 tff(2999,plain,
% 1.43/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[2998, 2996])).
% 1.43/1.60 tff(3000,plain,
% 1.43/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3001,plain,
% 1.43/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 1.43/1.60 tff(3002,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3001, 141, 2995, 2987, 2977])).
% 1.43/1.60 tff(3003,plain,((s(z) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3004,plain,
% 1.43/1.60 (s(z) = s(elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3003, 1366, 572, 1, 2562, 2824, 90])).
% 1.43/1.60 tff(3005,plain,
% 1.43/1.60 (s(s(z)) = s(s(elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3004])).
% 1.43/1.60 tff(3006,plain,
% 1.43/1.60 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3005])).
% 1.43/1.60 tff(3007,plain,
% 1.43/1.60 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[3006])).
% 1.43/1.60 tff(3008,plain,
% 1.43/1.60 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3006])).
% 1.43/1.60 tff(3009,plain,
% 1.43/1.60 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3008])).
% 1.43/1.60 tff(3010,plain,
% 1.43/1.60 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[3009])).
% 1.43/1.60 tff(3011,plain,
% 1.43/1.60 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3010, 3007])).
% 1.43/1.60 tff(3012,plain,
% 1.43/1.60 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[3011])).
% 1.43/1.60 tff(3013,plain,
% 1.43/1.60 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3010, 3007])).
% 1.43/1.60 tff(3014,plain,
% 1.43/1.60 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3013])).
% 1.43/1.60 tff(3015,assumption,(s(s(s(s(s(elem!1))))) = s(elem!1)), introduced(assumption)).
% 1.43/1.60 tff(3016,plain,
% 1.43/1.60 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[3015])).
% 1.43/1.60 tff(3017,plain,
% 1.43/1.60 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[3016, 1495])).
% 1.43/1.60 tff(3018,plain,
% 1.43/1.60 ((s(z) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[39])).
% 1.43/1.60 tff(3019,plain,
% 1.43/1.60 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3018])).
% 1.43/1.60 tff(3020,plain,
% 1.43/1.60 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[702, 3019])).
% 1.43/1.60 tff(3021,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3020, 3017])).
% 1.43/1.60 tff(3022,plain,((~(s(s(s(s(s(elem!1))))) = s(elem!1))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3023,plain,
% 1.43/1.60 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3022, 3004])).
% 1.43/1.60 tff(3024,assumption,(r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.43/1.60 tff(3025,plain,
% 1.43/1.60 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1495])).
% 1.43/1.60 tff(3026,plain,
% 1.43/1.60 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.60 inference(symmetry,[status(thm)],[3025])).
% 1.43/1.60 tff(3027,plain,
% 1.43/1.60 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.60 inference(transitivity,[status(thm)],[1650, 1470])).
% 1.43/1.60 tff(3028,plain,
% 1.43/1.60 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3027])).
% 1.43/1.60 tff(3029,plain,
% 1.43/1.60 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[734, 3028])).
% 1.43/1.60 tff(3030,plain,
% 1.43/1.60 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.60 inference(symmetry,[status(thm)],[2627])).
% 1.43/1.60 tff(3031,plain,
% 1.43/1.60 ((~r(s(s(s(s(s(elem!1))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3030])).
% 1.43/1.60 tff(3032,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2632, 141, 572, 1501, 3024])).
% 1.43/1.60 tff(3033,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3034,plain,
% 1.43/1.60 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3033, 3024, 572])).
% 1.43/1.60 tff(3035,plain,
% 1.43/1.60 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3034, 3031])).
% 1.43/1.60 tff(3036,plain,
% 1.43/1.60 (b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[787, 3035, 3029])).
% 1.43/1.60 tff(3037,plain,
% 1.43/1.60 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3036, 3026])).
% 1.43/1.60 tff(3038,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), s(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(X0, 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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3039,plain,
% 1.43/1.60 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3040,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3039])).
% 1.43/1.60 tff(3041,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[3040, 3038])).
% 1.43/1.60 tff(3042,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3043,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 1.43/1.60 tff(3044,plain,
% 1.43/1.60 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3043, 245, 1390, 2824, 3037])).
% 1.43/1.60 tff(3045,plain,
% 1.43/1.60 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1526, 32, 3044, 1523])).
% 1.43/1.60 tff(3046,plain,
% 1.43/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(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(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(elem!1))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3047,plain,
% 1.43/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3048,plain,
% 1.43/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3047, 3046])).
% 1.43/1.60 tff(3049,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3048, 141, 1366, 3045, 3024])).
% 1.43/1.60 tff(3050,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3051,plain,
% 1.43/1.60 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3050, 1366, 1490, 2839, 2824, 3004, 572])).
% 1.43/1.60 tff(3052,assumption,(~r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.43/1.60 tff(3053,assumption,(~(s(s(s(s(s(elem!1))))) = s(elem!1))), introduced(assumption)).
% 1.43/1.60 tff(3054,assumption,(~b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.43/1.60 tff(3055,plain,
% 1.43/1.60 (((~![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)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(3056,plain,
% 1.43/1.60 ((~![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)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(3057,plain,
% 1.43/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3056, 3055])).
% 1.43/1.60 tff(3058,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3057, 32, 3054, 3053, 3052])).
% 1.43/1.60 tff(3059,plain,(r(s(s(s(s(s(elem!1))))), s(elem!1)) | b(s(s(s(s(s(elem!1))))), s(elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(3060,plain,
% 1.43/1.60 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3059, 3051, 3023])).
% 1.43/1.60 tff(3061,plain,
% 1.43/1.60 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3004])).
% 1.43/1.60 tff(3062,plain,
% 1.43/1.60 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3004])).
% 1.43/1.60 tff(3063,plain,
% 1.43/1.60 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[3062])).
% 1.43/1.60 tff(3064,plain,
% 1.43/1.60 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[3063])).
% 1.43/1.60 tff(3065,plain,
% 1.43/1.60 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1571, 3004, 1])).
% 1.43/1.60 tff(3066,plain,
% 1.43/1.60 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3022, 39])).
% 1.43/1.60 tff(3067,plain,
% 1.43/1.60 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1311, 1309])).
% 1.43/1.60 tff(3068,plain,
% 1.43/1.60 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1489, 3067])).
% 1.43/1.60 tff(3069,plain,
% 1.43/1.60 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1507, 141, 170, 1501])).
% 1.43/1.60 tff(3070,plain,
% 1.43/1.60 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3069, 1500])).
% 1.43/1.60 tff(3071,plain,
% 1.43/1.60 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1515, 3070])).
% 1.43/1.60 tff(3072,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3071, 1498])).
% 1.43/1.60 tff(3073,plain,
% 1.43/1.60 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[2632, 141, 572, 1501])).
% 1.43/1.60 tff(3074,plain,
% 1.43/1.60 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[3059, 3073, 3066])).
% 1.43/1.60 tff(3075,plain,
% 1.43/1.60 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[39])).
% 1.43/1.60 tff(3076,plain,
% 1.43/1.60 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.43/1.60 inference(symmetry,[status(thm)],[3075])).
% 1.43/1.60 tff(3077,plain,
% 1.43/1.60 (r(s(z), elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[572, 3076])).
% 1.43/1.60 tff(3078,plain,
% 1.43/1.60 (~r(s(z), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1143, 170, 3077])).
% 1.43/1.60 tff(3079,plain,
% 1.43/1.60 (b(s(z), s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1133, 3078])).
% 1.43/1.60 tff(3080,plain,
% 1.43/1.60 (b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[3079, 1781])).
% 1.43/1.61 tff(3081,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3082,plain,
% 1.43/1.61 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3083,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3082])).
% 1.43/1.61 tff(3084,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3083, 3081])).
% 1.43/1.61 tff(3085,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3086,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 1.43/1.61 tff(3087,plain,
% 1.43/1.61 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3086, 245, 1287, 3080, 3074])).
% 1.43/1.61 tff(3088,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3087, 3072])).
% 1.43/1.61 tff(3089,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3090,plain,
% 1.43/1.61 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3089, 170, 1287, 39, 572])).
% 1.43/1.61 tff(3091,plain,
% 1.43/1.61 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3090, 3031])).
% 1.43/1.61 tff(3092,plain,
% 1.43/1.61 (b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[787, 3091, 3029])).
% 1.43/1.61 tff(3093,plain,
% 1.43/1.61 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3092, 3026])).
% 1.43/1.61 tff(3094,plain,
% 1.43/1.61 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3043, 245, 1390, 2824, 3093])).
% 1.43/1.61 tff(3095,plain,
% 1.43/1.61 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1526, 32, 3094, 3068])).
% 1.43/1.61 tff(3096,plain,
% 1.43/1.61 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3048, 141, 1366, 3095])).
% 1.43/1.61 tff(3097,plain,
% 1.43/1.61 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3059, 3096, 3066])).
% 1.43/1.61 tff(3098,plain,
% 1.43/1.61 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3086, 245, 1287, 3080, 3097])).
% 1.43/1.61 tff(3099,plain,
% 1.43/1.61 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3098, 1610])).
% 1.43/1.61 tff(3100,plain,
% 1.43/1.61 (s(z) = s(elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[117, 114])).
% 1.43/1.61 tff(3101,plain,
% 1.43/1.61 (s(s(z)) = s(s(elem!1))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3100])).
% 1.43/1.61 tff(3102,plain,
% 1.43/1.61 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3101])).
% 1.43/1.61 tff(3103,plain,
% 1.43/1.61 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3102])).
% 1.43/1.61 tff(3104,plain,
% 1.43/1.61 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3103])).
% 1.43/1.61 tff(3105,plain,
% 1.43/1.61 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[3104])).
% 1.43/1.61 tff(3106,plain,
% 1.43/1.61 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.43/1.61 inference(symmetry,[status(thm)],[3102])).
% 1.43/1.61 tff(3107,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3106, 3105])).
% 1.43/1.61 tff(3108,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[3107])).
% 1.43/1.61 tff(3109,plain,
% 1.43/1.61 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3106, 3105])).
% 1.43/1.61 tff(3110,plain,
% 1.43/1.61 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3109])).
% 1.43/1.61 tff(3111,assumption,(b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.43/1.61 tff(3112,plain,
% 1.43/1.61 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3086, 245, 1287, 2939])).
% 1.43/1.61 tff(3113,plain,
% 1.43/1.61 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3112, 3111])).
% 1.43/1.61 tff(3114,plain,
% 1.43/1.61 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3113, 3110])).
% 1.43/1.61 tff(3115,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1515, 3114])).
% 1.43/1.61 tff(3116,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3115, 3108])).
% 1.43/1.61 tff(3117,plain,
% 1.43/1.61 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3105])).
% 1.43/1.61 tff(3118,plain,
% 1.43/1.61 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[3117])).
% 1.43/1.61 tff(3119,plain,
% 1.43/1.61 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.61 tff(3120,plain,
% 1.43/1.61 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3119, 770])).
% 1.43/1.61 tff(3121,plain,
% 1.43/1.61 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3120])).
% 1.43/1.61 tff(3122,plain,
% 1.43/1.61 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[734, 3121])).
% 1.43/1.61 tff(3123,plain,
% 1.43/1.61 (b(z, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[114, 3105])).
% 1.43/1.61 tff(3124,plain,
% 1.43/1.61 (elem!1 = z),
% 1.43/1.61 inference(symmetry,[status(thm)],[114])).
% 1.43/1.61 tff(3125,plain,
% 1.43/1.61 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3124])).
% 1.43/1.61 tff(3126,plain,
% 1.43/1.61 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3125, 3123])).
% 1.43/1.61 tff(3127,plain,
% 1.43/1.61 ((~b(elem!1, s(s(s(s(s(elem!1))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3126])).
% 1.43/1.61 tff(3128,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3129,plain,
% 1.43/1.61 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3130,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3129])).
% 1.43/1.61 tff(3131,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3130, 3128])).
% 1.43/1.61 tff(3132,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3133,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3132, 3131])).
% 1.43/1.61 tff(3134,plain,
% 1.43/1.61 ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3133, 245, 1287, 2939, 1103])).
% 1.43/1.61 tff(3135,plain,
% 1.43/1.61 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3134, 3111])).
% 1.43/1.61 tff(3136,plain,
% 1.43/1.61 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3135, 3127])).
% 1.43/1.61 tff(3137,plain,
% 1.43/1.61 (r(elem!1, s(s(s(s(s(z))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[720, 3136, 3122])).
% 1.43/1.61 tff(3138,plain,
% 1.43/1.61 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3137, 3118])).
% 1.43/1.61 tff(3139,plain,
% 1.43/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(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(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3140,plain,
% 1.43/1.61 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3141,plain,
% 1.43/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(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(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3140])).
% 1.43/1.61 tff(3142,plain,
% 1.43/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(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(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3141, 3139])).
% 1.43/1.61 tff(3143,plain,
% 1.43/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3144,plain,
% 1.43/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3143, 3142])).
% 1.43/1.61 tff(3145,plain,
% 1.43/1.61 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3144, 141, 170, 3138])).
% 1.43/1.61 tff(3146,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3145, 3116])).
% 1.43/1.61 tff(3147,plain,((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3148,plain,
% 1.43/1.61 (~b(elem!1, s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3147, 3097, 58, 3080, 1287, 170])).
% 1.43/1.61 tff(3149,plain,
% 1.43/1.61 (r(elem!1, s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2777, 3148, 2774])).
% 1.43/1.61 tff(3150,plain,
% 1.43/1.61 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[2690, 1523])).
% 1.43/1.61 tff(3151,plain,
% 1.43/1.61 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3150, 2680])).
% 1.43/1.61 tff(3152,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(elem!1))), introduced(assumption)).
% 1.43/1.61 tff(3153,plain,
% 1.43/1.61 (((~![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(elem!1)))))), s(elem!1))) | (~r(s(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(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3154,plain,
% 1.43/1.61 ((~![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(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3155,plain,
% 1.43/1.61 ((~![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(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3154, 3153])).
% 1.43/1.61 tff(3156,plain,
% 1.43/1.61 ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3155, 141, 406])).
% 1.43/1.61 tff(3157,plain,
% 1.43/1.61 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3156, 3152])).
% 1.43/1.61 tff(3158,plain,
% 1.43/1.61 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[501, 3157, 2193])).
% 1.43/1.61 tff(3159,plain,
% 1.43/1.61 (((~![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(elem!1)))))), s(elem!1))) | (~r(s(s(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(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3160,plain,
% 1.43/1.61 ((~![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(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3161,plain,
% 1.43/1.61 ((~![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(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3160, 3159])).
% 1.43/1.61 tff(3162,plain,
% 1.43/1.61 ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3161, 141, 1367])).
% 1.43/1.61 tff(3163,plain,
% 1.43/1.61 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3162, 3152])).
% 1.43/1.61 tff(3164,plain,
% 1.43/1.61 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1768, 3163, 1855])).
% 1.43/1.61 tff(3165,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(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(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3166,plain,
% 1.43/1.61 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(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(s(elem!1)))))), elem!1)) | (~b(s(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3167,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(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(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3166])).
% 1.43/1.61 tff(3168,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(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(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3167, 3165])).
% 1.43/1.61 tff(3169,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3170,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 1.43/1.61 tff(3171,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3170, 245, 1390, 2824, 3164, 3158])).
% 1.43/1.61 tff(3172,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(3173,plain,
% 1.43/1.61 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3172, 406, 1555, 2193, 2824, 1367, 1390])).
% 1.43/1.61 tff(3174,plain,
% 1.43/1.61 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3173, 1780])).
% 1.43/1.61 tff(3175,plain,
% 1.43/1.61 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1820, 3174])).
% 1.43/1.61 tff(3176,plain,
% 1.43/1.61 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3175, 1544])).
% 1.43/1.61 tff(3177,plain,
% 1.43/1.61 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1496])).
% 1.43/1.61 tff(3178,plain,
% 1.43/1.61 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[3177])).
% 1.43/1.61 tff(3179,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(elem!1))), introduced(assumption)).
% 1.43/1.61 tff(3180,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3181,plain,
% 1.43/1.61 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(3182,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1)))))), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[3181])).
% 1.43/1.61 tff(3183,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1)))))), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[3182, 3180])).
% 1.43/1.61 tff(3184,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(3185,plain,
% 1.43/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 1.43/1.61 tff(3186,plain,
% 1.43/1.61 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3185, 245, 1287, 2939])).
% 1.43/1.61 tff(3187,plain,
% 1.43/1.61 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[3186, 3179])).
% 1.43/1.61 tff(3188,plain,
% 1.43/1.61 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3187, 1618])).
% 1.43/1.61 tff(3189,plain,
% 1.43/1.61 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1630, 3188, 1616])).
% 1.43/1.61 tff(3190,plain,
% 1.43/1.61 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[3189, 3178])).
% 1.43/1.61 tff(3191,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3192,plain,
% 1.43/1.62 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3193,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3192])).
% 1.43/1.62 tff(3194,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3193, 3191])).
% 1.43/1.62 tff(3195,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3196,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 1.43/1.62 tff(3197,plain,
% 1.43/1.62 ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3196, 245, 1287, 2939, 3111])).
% 1.43/1.62 tff(3198,plain,
% 1.43/1.62 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3197, 3179])).
% 1.43/1.62 tff(3199,plain,
% 1.43/1.62 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1607, 32, 1542, 3198])).
% 1.43/1.62 tff(3200,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3201,plain,
% 1.43/1.62 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3202,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3201])).
% 1.43/1.62 tff(3203,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3202, 3200])).
% 1.43/1.62 tff(3204,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3205,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.43/1.62 tff(3206,plain,
% 1.43/1.62 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3205, 245, 1287, 2939, 3111])).
% 1.43/1.62 tff(3207,plain,
% 1.43/1.62 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3206, 1658])).
% 1.43/1.62 tff(3208,plain,
% 1.43/1.62 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[909, 3207])).
% 1.43/1.62 tff(3209,plain,
% 1.43/1.62 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3208, 1656])).
% 1.43/1.62 tff(3210,plain,
% 1.43/1.62 (((~![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(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(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(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3211,plain,
% 1.43/1.62 ((~![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(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3212,plain,
% 1.43/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3211, 3210])).
% 1.43/1.62 tff(3213,plain,
% 1.43/1.62 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3212, 141, 3209, 3199])).
% 1.43/1.62 tff(3214,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3213, 3190])).
% 1.43/1.62 tff(3215,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(3216,plain,
% 1.43/1.62 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3215, 3176, 1616, 1287, 3151, 2939, 39])).
% 1.43/1.62 tff(3217,plain,
% 1.43/1.62 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3059, 3216, 3066])).
% 1.43/1.62 tff(3218,plain,
% 1.43/1.62 (((~![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(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(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3219,plain,
% 1.43/1.62 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3220,plain,
% 1.43/1.62 (((~![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(elem!1))))), s(elem!1))) | (~r(s(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(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3219])).
% 1.43/1.62 tff(3221,plain,
% 1.43/1.62 (((~![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(elem!1))))), s(elem!1))) | (~r(s(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(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3220, 3218])).
% 1.43/1.62 tff(3222,plain,
% 1.43/1.62 ((~![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(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3223,plain,
% 1.43/1.62 ((~![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(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3222, 3221])).
% 1.43/1.62 tff(3224,plain,
% 1.43/1.62 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3223, 141, 1367, 3217])).
% 1.43/1.62 tff(3225,plain,
% 1.43/1.62 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3224, 3031])).
% 1.43/1.62 tff(3226,plain,
% 1.43/1.62 (b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[787, 3225, 3029])).
% 1.43/1.62 tff(3227,plain,
% 1.43/1.62 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3226, 3026])).
% 1.43/1.62 tff(3228,plain,
% 1.43/1.62 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1593, 141, 406, 3217])).
% 1.43/1.62 tff(3229,plain,
% 1.43/1.62 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1526, 32, 1523, 3228])).
% 1.43/1.62 tff(3230,plain,
% 1.43/1.62 (((~b(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(elem!1)))), elem!1)) | (~b(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))))), 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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3231,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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))))), s(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(X0, 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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3230])).
% 1.43/1.62 tff(3232,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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))))), s(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(X0, 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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3231, 3038])).
% 1.43/1.62 tff(3233,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3234,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3233, 3232])).
% 1.43/1.62 tff(3235,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3234, 245, 1390, 2824, 3229, 3227])).
% 1.43/1.62 tff(3236,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(3237,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3236, 3149, 2824, 39, 3068, 1390, 1616, 1287, 3080, 2193])).
% 1.43/1.62 tff(3238,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[420, 3237, 164])).
% 1.43/1.62 tff(3239,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3240,plain,
% 1.43/1.62 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(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(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3241,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3240])).
% 1.43/1.62 tff(3242,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3241, 3239])).
% 1.43/1.62 tff(3243,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3244,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 1.43/1.62 tff(3245,plain,
% 1.43/1.62 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3244, 245, 1287, 3080, 3238])).
% 1.43/1.62 tff(3246,plain,
% 1.43/1.62 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1239, 3245, 1309])).
% 1.43/1.62 tff(3247,plain,
% 1.43/1.62 (((~![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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3248,plain,
% 1.43/1.62 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3249,plain,
% 1.43/1.62 (((~![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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3248])).
% 1.43/1.62 tff(3250,plain,
% 1.43/1.62 (((~![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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3249, 3247])).
% 1.43/1.62 tff(3251,plain,
% 1.43/1.62 ((~![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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3252,plain,
% 1.43/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3251, 3250])).
% 1.43/1.62 tff(3253,plain,
% 1.43/1.62 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3252, 141, 3246, 3095])).
% 1.43/1.62 tff(3254,plain,
% 1.43/1.62 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3253, 1500])).
% 1.43/1.62 tff(3255,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1515, 3254, 3099])).
% 1.43/1.62 tff(3256,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(3257,plain,
% 1.43/1.62 (~r(s(s(s(elem!1))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3256, 3004, 2855, 1304, 7, 2824, 2839, 3065, 2699, 2563, 1366, 572])).
% 1.43/1.62 tff(3258,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[110, 3257, 96])).
% 1.43/1.62 tff(3259,plain,
% 1.43/1.62 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2849, 3258, 2824, 2839])).
% 1.43/1.62 tff(3260,plain,
% 1.43/1.62 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1239, 3259, 1304])).
% 1.43/1.62 tff(3261,plain,
% 1.43/1.62 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2357, 3260, 1366])).
% 1.43/1.62 tff(3262,plain,
% 1.43/1.62 (~r(s(z), s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3261, 3064])).
% 1.43/1.62 tff(3263,plain,
% 1.43/1.62 (b(s(z), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1133, 3262])).
% 1.43/1.62 tff(3264,plain,
% 1.43/1.62 (b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3263, 3061])).
% 1.43/1.62 tff(3265,plain,
% 1.43/1.62 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3205, 245, 2855, 3264, 3060])).
% 1.43/1.62 tff(3266,plain,
% 1.43/1.62 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3265, 3014])).
% 1.43/1.62 tff(3267,plain,
% 1.43/1.62 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[909, 3266])).
% 1.43/1.62 tff(3268,plain,
% 1.43/1.62 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3267, 3012])).
% 1.43/1.62 tff(3269,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3270,plain,
% 1.43/1.62 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(3271,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[3270])).
% 1.43/1.62 tff(3272,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[3271, 3269])).
% 1.43/1.62 tff(3273,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(3274,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3273, 3272])).
% 1.43/1.62 tff(3275,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3274, 245, 1287, 2939, 1427, 1103])).
% 1.43/1.62 tff(3276,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(3277,plain,
% 1.43/1.62 (~b(elem!1, s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3276, 2855, 3264, 3258])).
% 1.43/1.62 tff(3278,plain,
% 1.43/1.62 (r(elem!1, s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[2777, 3277, 2563])).
% 1.43/1.62 tff(3279,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[3236, 3278, 2824, 3004, 1490, 2839, 3065, 2855, 3264, 2699])).
% 1.43/1.62 tff(3280,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[420, 3279, 7])).
% 1.43/1.62 tff(3281,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3282,plain,
% 1.43/1.63 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3283,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[3282])).
% 1.43/1.63 tff(3284,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[3283, 3281])).
% 1.43/1.63 tff(3285,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3286,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3285, 3284])).
% 1.43/1.63 tff(3287,plain,
% 1.43/1.63 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3286, 245, 2855, 3264, 3280, 3060])).
% 1.43/1.63 tff(3288,plain,
% 1.43/1.63 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1526, 32, 3287, 1490])).
% 1.43/1.63 tff(3289,plain,
% 1.43/1.63 (((~![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(s(s(elem!1))))), 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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3290,plain,
% 1.43/1.63 ((~![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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3291,plain,
% 1.43/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3290, 3289])).
% 1.43/1.63 tff(3292,plain,
% 1.43/1.63 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3291, 141, 3260, 3288])).
% 1.43/1.63 tff(3293,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3292, 3268])).
% 1.43/1.63 tff(3294,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(3295,plain,
% 1.43/1.63 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3294, 2823, 1277, 1, 2562, 90])).
% 1.43/1.63 tff(3296,plain,
% 1.43/1.63 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1263, 3295, 1])).
% 1.43/1.63 tff(3297,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3298,plain,
% 1.43/1.63 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3299,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[3298])).
% 1.43/1.63 tff(3300,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[3299, 3297])).
% 1.43/1.63 tff(3301,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3302,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3301, 3300])).
% 1.43/1.63 tff(3303,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3302, 245, 288, 838, 556, 1943])).
% 1.43/1.63 tff(3304,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(3305,plain,
% 1.43/1.63 (~b(s(s(s(s(elem!1)))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3304, 2827, 556, 2829])).
% 1.43/1.63 tff(3306,plain,
% 1.43/1.63 (r(s(s(s(s(elem!1)))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[2558, 3305])).
% 1.43/1.63 tff(3307,plain,
% 1.43/1.63 (~r(s(s(s(elem!1))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[577, 371, 572])).
% 1.43/1.63 tff(3308,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[110, 3307, 96])).
% 1.43/1.63 tff(3309,plain,
% 1.43/1.63 (~b(s(s(s(s(elem!1)))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3304, 645, 556, 2938])).
% 1.43/1.63 tff(3310,plain,
% 1.43/1.63 (r(s(s(s(s(elem!1)))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[2558, 3309])).
% 1.43/1.63 tff(3311,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3312,plain,
% 1.43/1.63 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3313,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[3312])).
% 1.43/1.63 tff(3314,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[3313, 3311])).
% 1.43/1.63 tff(3315,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3316,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 1.43/1.63 tff(3317,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3316, 245, 1427, 2101, 2824, 1276])).
% 1.43/1.63 tff(3318,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(3319,plain,
% 1.43/1.63 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3318, 2101, 2824, 3308])).
% 1.43/1.63 tff(3320,plain,
% 1.43/1.63 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1239, 3319, 1304])).
% 1.43/1.63 tff(3321,plain,
% 1.43/1.63 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[415, 3320, 371])).
% 1.43/1.63 tff(3322,plain,
% 1.43/1.63 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[420, 3321, 7])).
% 1.43/1.63 tff(3323,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3324,plain,
% 1.43/1.63 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3325,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[3324])).
% 1.43/1.63 tff(3326,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[3325, 3323])).
% 1.43/1.63 tff(3327,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3328,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 1.43/1.63 tff(3329,plain,
% 1.43/1.63 (~b(z, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3328, 245, 2938, 645, 3322])).
% 1.43/1.63 tff(3330,plain,
% 1.43/1.63 (r(z, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1992, 3329])).
% 1.43/1.63 tff(3331,plain,
% 1.43/1.63 (((~![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(s(s(elem!1)))))) | (~r(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))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3332,plain,
% 1.43/1.63 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3333,plain,
% 1.43/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[3332])).
% 1.43/1.63 tff(3334,plain,
% 1.43/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(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(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[3333, 3331])).
% 1.43/1.63 tff(3335,plain,
% 1.43/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3336,plain,
% 1.43/1.63 ((~![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(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3335, 3334])).
% 1.43/1.63 tff(3337,plain,
% 1.43/1.63 (~r(s(s(s(elem!1))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3336, 141, 3330, 3320])).
% 1.43/1.63 tff(3338,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[37, 3337])).
% 1.43/1.63 tff(3339,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3340,plain,
% 1.43/1.63 (((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3341,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[3340])).
% 1.43/1.63 tff(3342,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[3341, 3339])).
% 1.43/1.63 tff(3343,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3344,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3343, 3342])).
% 1.43/1.63 tff(3345,plain,
% 1.43/1.63 (~b(s(s(s(elem!1))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3344, 245, 234, 355, 288, 838])).
% 1.43/1.63 tff(3346,plain,
% 1.43/1.63 (~b(s(z), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[663, 355, 572, 289])).
% 1.43/1.63 tff(3347,plain,
% 1.43/1.63 (r(s(z), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[440, 3346, 9])).
% 1.43/1.63 tff(3348,plain,
% 1.43/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3349,plain,
% 1.43/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3350,plain,
% 1.43/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3349, 3348])).
% 1.43/1.63 tff(3351,plain,
% 1.43/1.63 (~r(s(s(s(elem!1))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3350, 141, 371, 3347])).
% 1.43/1.63 tff(3352,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[265, 3351, 3345])).
% 1.43/1.63 tff(3353,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(3354,plain,
% 1.43/1.63 (~b(s(z), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3353, 3338, 371, 2938, 645, 9, 572, 289])).
% 1.43/1.63 tff(3355,plain,
% 1.43/1.63 (r(s(z), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[232, 3354])).
% 1.43/1.63 tff(3356,plain,
% 1.43/1.63 (((~![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(z, s(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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(3357,plain,
% 1.43/1.63 ((~![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(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(3358,plain,
% 1.43/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[3357, 3356])).
% 1.43/1.63 tff(3359,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[3358, 141, 2069, 310, 407])).
% 1.43/1.64 tff(3360,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(3361,plain,
% 1.43/1.64 (~r(z, s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3360, 3330, 3320])).
% 1.43/1.64 tff(3362,plain,
% 1.43/1.64 (b(z, s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[197, 3361])).
% 1.43/1.64 tff(3363,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3364,plain,
% 1.43/1.64 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3365,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3364])).
% 1.43/1.64 tff(3366,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[3365, 3363])).
% 1.43/1.64 tff(3367,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3368,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3367, 3366])).
% 1.43/1.64 tff(3369,plain,
% 1.43/1.64 (~b(elem!1, z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3368, 245, 3308, 3362, 2101])).
% 1.43/1.64 tff(3370,plain,
% 1.43/1.64 (r(elem!1, z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[128, 3369, 124])).
% 1.43/1.64 tff(3371,plain,
% 1.43/1.64 (~r(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2099, 141, 3370, 3355])).
% 1.43/1.64 tff(3372,plain,
% 1.43/1.64 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[225, 3355, 106])).
% 1.43/1.64 tff(3373,plain,
% 1.43/1.64 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[217, 3372])).
% 1.43/1.64 tff(3374,plain,
% 1.43/1.64 (((~![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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3375,plain,
% 1.43/1.64 ((~![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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3376,plain,
% 1.43/1.64 ((~![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(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3375, 3374])).
% 1.43/1.64 tff(3377,plain,
% 1.43/1.64 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3376, 141, 3355, 106])).
% 1.43/1.64 tff(3378,plain,
% 1.43/1.64 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2448, 32, 3377])).
% 1.43/1.64 tff(3379,plain,
% 1.43/1.64 (b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3378, 2438])).
% 1.43/1.64 tff(3380,assumption,(b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.64 tff(3381,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3382,plain,
% 1.43/1.64 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3383,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3382])).
% 1.43/1.64 tff(3384,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[3383, 3381])).
% 1.43/1.64 tff(3385,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3386,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3385, 3384])).
% 1.43/1.64 tff(3387,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3386, 245, 301, 2824, 2653, 3380])).
% 1.43/1.64 tff(3388,plain,((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(3389,plain,
% 1.43/1.64 (~b(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3388, 3379, 2824, 3373])).
% 1.43/1.64 tff(3390,plain,
% 1.43/1.64 (elem!1 = s(z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[281, 3389, 3371])).
% 1.43/1.64 tff(3391,plain,
% 1.43/1.64 (s(elem!1) = s(s(z))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3390])).
% 1.43/1.64 tff(3392,plain,
% 1.43/1.64 (s(s(elem!1)) = s(s(s(z)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3391])).
% 1.43/1.64 tff(3393,plain,
% 1.43/1.64 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3392])).
% 1.43/1.64 tff(3394,plain,
% 1.43/1.64 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3393])).
% 1.43/1.64 tff(3395,plain,
% 1.43/1.64 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3394])).
% 1.43/1.64 tff(3396,plain,
% 1.43/1.64 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3395])).
% 1.43/1.64 tff(3397,plain,
% 1.43/1.64 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3396])).
% 1.43/1.64 tff(3398,plain,
% 1.43/1.64 ((z = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = z)),
% 1.43/1.64 inference(commutativity,[status(thm)],[])).
% 1.43/1.64 tff(3399,plain,
% 1.43/1.64 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (z = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3398])).
% 1.43/1.64 tff(3400,plain,
% 1.43/1.64 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(z = s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3399])).
% 1.43/1.64 tff(3401,plain,
% 1.43/1.64 (~(z = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1554, 3400])).
% 1.43/1.64 tff(3402,plain,
% 1.43/1.64 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3390])).
% 1.43/1.64 tff(3403,plain,
% 1.43/1.64 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3390])).
% 1.43/1.64 tff(3404,plain,
% 1.43/1.64 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3403])).
% 1.43/1.64 tff(3405,plain,
% 1.43/1.64 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.43/1.64 inference(transitivity,[status(thm)],[3404, 1548])).
% 1.43/1.64 tff(3406,plain,
% 1.43/1.64 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3405])).
% 1.43/1.64 tff(3407,plain,
% 1.43/1.64 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[465, 3406])).
% 1.43/1.64 tff(3408,plain,
% 1.43/1.64 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3393])).
% 1.43/1.64 tff(3409,plain,
% 1.43/1.64 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[3408, 2135])).
% 1.43/1.64 tff(3410,plain,
% 1.43/1.64 ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3409])).
% 1.43/1.64 tff(3411,plain,
% 1.43/1.64 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3410])).
% 1.43/1.64 tff(3412,plain,
% 1.43/1.64 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2156, 3390, 1])).
% 1.43/1.64 tff(3413,plain,
% 1.43/1.64 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2163, 3412])).
% 1.43/1.64 tff(3414,plain,
% 1.43/1.64 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3413, 3411])).
% 1.43/1.64 tff(3415,plain,
% 1.43/1.64 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2930, 3414, 2101, 2193, 3308, 3320, 2824])).
% 1.43/1.64 tff(3416,plain,
% 1.43/1.64 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1768, 3415, 3407])).
% 1.43/1.64 tff(3417,plain,
% 1.43/1.64 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3416, 3402])).
% 1.43/1.64 tff(3418,plain,
% 1.43/1.64 (r(z, elem!1) <=> r(z, s(z))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3390])).
% 1.43/1.64 tff(3419,plain,
% 1.43/1.64 (r(z, s(z))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[289, 3418])).
% 1.43/1.64 tff(3420,plain,
% 1.43/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(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(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3421,plain,
% 1.43/1.64 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3422,plain,
% 1.43/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3421])).
% 1.43/1.64 tff(3423,plain,
% 1.43/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[3422, 3420])).
% 1.43/1.64 tff(3424,plain,
% 1.43/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3425,plain,
% 1.43/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 1.43/1.64 tff(3426,plain,
% 1.43/1.64 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3425, 141, 3419, 3417])).
% 1.43/1.64 tff(3427,plain,
% 1.43/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3428,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3429,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3428, 3427])).
% 1.43/1.64 tff(3430,plain,
% 1.43/1.64 ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3429, 32, 3426])).
% 1.43/1.64 tff(3431,plain,
% 1.43/1.64 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3430, 3401])).
% 1.43/1.64 tff(3432,plain,
% 1.43/1.64 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2216, 141, 3419, 3417])).
% 1.43/1.64 tff(3433,plain,
% 1.43/1.64 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2220, 32, 1554, 3432])).
% 1.43/1.64 tff(3434,plain,
% 1.43/1.64 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3391])).
% 1.43/1.64 tff(3435,plain,
% 1.43/1.64 (b(s(s(z)), z)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[2938, 3434])).
% 1.43/1.64 tff(3436,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3437,plain,
% 1.43/1.64 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3438,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3437])).
% 1.43/1.64 tff(3439,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[3438, 3436])).
% 1.43/1.64 tff(3440,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3441,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3440, 3439])).
% 1.43/1.64 tff(3442,plain,
% 1.43/1.64 (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3441, 245, 3435, 3433, 3431])).
% 1.43/1.64 tff(3443,plain,
% 1.43/1.64 (s(s(z)) = s(elem!1)),
% 1.43/1.64 inference(symmetry,[status(thm)],[3391])).
% 1.43/1.64 tff(3444,plain,
% 1.43/1.64 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3443])).
% 1.43/1.64 tff(3445,plain,
% 1.43/1.64 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3444])).
% 1.43/1.64 tff(3446,plain,
% 1.43/1.64 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3390])).
% 1.43/1.64 tff(3447,plain,
% 1.43/1.64 (r(s(elem!1), s(z))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[572, 3446])).
% 1.43/1.64 tff(3448,plain,
% 1.43/1.64 (r(s(s(z)), s(z))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3447, 3445])).
% 1.43/1.64 tff(3449,plain,
% 1.43/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(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(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3450,plain,
% 1.43/1.64 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(z))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3451,plain,
% 1.43/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(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(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3450])).
% 1.43/1.64 tff(3452,plain,
% 1.43/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(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(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(z))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[3451, 3449])).
% 1.43/1.64 tff(3453,plain,
% 1.43/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3454,plain,
% 1.43/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(z)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 1.43/1.64 tff(3455,plain,
% 1.43/1.64 ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(z)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3454, 141, 3417])).
% 1.43/1.64 tff(3456,plain,
% 1.43/1.64 (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3455, 3448])).
% 1.43/1.64 tff(3457,plain,
% 1.43/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3458,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3459,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[3458, 3457])).
% 1.43/1.64 tff(3460,plain,
% 1.43/1.64 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3459, 32, 3456])).
% 1.43/1.64 tff(3461,plain,
% 1.43/1.64 (s(s(z)) = s(s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3460, 3442])).
% 1.43/1.64 tff(3462,plain,
% 1.43/1.64 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3461])).
% 1.43/1.64 tff(3463,plain,
% 1.43/1.64 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(z)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3462])).
% 1.43/1.64 tff(3464,plain,
% 1.43/1.64 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3463])).
% 1.43/1.64 tff(3465,plain,
% 1.43/1.64 (s(z) = s(s(s(s(s(s(z))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[591, 3464, 320, 3397])).
% 1.43/1.64 tff(3466,plain,
% 1.43/1.64 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3465])).
% 1.43/1.64 tff(3467,plain,
% 1.43/1.64 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.43/1.64 inference(symmetry,[status(thm)],[3466])).
% 1.43/1.64 tff(3468,plain,
% 1.43/1.64 (s(s(s(s(s(z))))) = z),
% 1.43/1.64 inference(transitivity,[status(thm)],[2278, 3467, 52])).
% 1.43/1.64 tff(3469,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[734, 3468])).
% 1.43/1.64 tff(3470,plain,((~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(3471,plain,
% 1.43/1.64 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3470, 371, 2824, 572, 289, 1, 3310, 2498, 9])).
% 1.43/1.64 tff(3472,plain,
% 1.43/1.64 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1724, 3471, 1673])).
% 1.43/1.64 tff(3473,plain,
% 1.43/1.64 (~r(elem!1, s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2762, 3472, 371])).
% 1.43/1.64 tff(3474,plain,
% 1.43/1.64 (b(elem!1, s(elem!1))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[2777, 3473, 2563])).
% 1.43/1.64 tff(3475,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), 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(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3476,plain,
% 1.43/1.64 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(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(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))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(3477,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(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(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[3476])).
% 1.43/1.64 tff(3478,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(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(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[3477, 3475])).
% 1.43/1.64 tff(3479,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(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)))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(3480,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3479, 3478])).
% 1.43/1.65 tff(3481,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3480, 245, 1427, 1103, 2824, 556, 1276])).
% 1.43/1.65 tff(3482,plain,((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(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))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3483,plain,
% 1.43/1.65 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3482, 3474, 2824, 3308, 556])).
% 1.43/1.65 tff(3484,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2395, 3474, 399, 371, 3472, 1])).
% 1.43/1.65 tff(3485,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1239, 3484, 3483, 1304])).
% 1.43/1.65 tff(3486,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (elem!1 = s(s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3487,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3486, 176, 1, 2824, 556, 572, 399, 9])).
% 1.43/1.65 tff(3488,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[353, 3487, 2338])).
% 1.43/1.65 tff(3489,plain,
% 1.43/1.65 (~b(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2871, 245, 3488, 2829, 2827])).
% 1.43/1.65 tff(3490,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[37, 3489])).
% 1.43/1.65 tff(3491,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2875, 3490, 176])).
% 1.43/1.65 tff(3492,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[110, 3491, 96])).
% 1.43/1.65 tff(3493,plain,
% 1.43/1.65 (~b(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2861, 245, 3488, 2829, 2827])).
% 1.43/1.65 tff(3494,plain,
% 1.43/1.65 (r(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[197, 3493])).
% 1.43/1.65 tff(3495,plain,
% 1.43/1.65 (~r(elem!1, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2078, 3494, 176])).
% 1.43/1.65 tff(3496,plain,
% 1.43/1.65 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1724, 3495, 1673])).
% 1.43/1.65 tff(3497,plain,
% 1.43/1.65 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3318, 3496, 2824, 3492])).
% 1.43/1.65 tff(3498,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1239, 3497, 1304])).
% 1.43/1.65 tff(3499,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1361, 141, 3490, 3498, 3306])).
% 1.43/1.65 tff(3500,plain,((s(z) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3501,plain,
% 1.43/1.65 (s(z) = s(elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3500, 2823, 1, 3296, 1277, 2568, 90])).
% 1.43/1.65 tff(3502,plain,
% 1.43/1.65 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3501])).
% 1.43/1.65 tff(3503,plain,
% 1.43/1.65 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.65 inference(symmetry,[status(thm)],[3502])).
% 1.43/1.65 tff(3504,plain,
% 1.43/1.65 ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3503])).
% 1.43/1.65 tff(3505,plain,
% 1.43/1.65 (z = elem!1),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[57, 3501])).
% 1.43/1.65 tff(3506,plain,
% 1.43/1.65 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3505])).
% 1.43/1.65 tff(3507,plain,
% 1.43/1.65 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3506, 1547])).
% 1.43/1.65 tff(3508,plain,
% 1.43/1.65 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.43/1.65 inference(transitivity,[status(thm)],[3507, 1548])).
% 1.43/1.65 tff(3509,plain,
% 1.43/1.65 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3508])).
% 1.43/1.65 tff(3510,plain,
% 1.43/1.65 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1554, 3509])).
% 1.43/1.65 tff(3511,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[577, 170, 1277])).
% 1.43/1.65 tff(3512,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[353, 3511, 11])).
% 1.43/1.65 tff(3513,plain,
% 1.43/1.65 (r(s(z), elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1277, 3076])).
% 1.43/1.65 tff(3514,plain,
% 1.43/1.65 (~r(s(z), s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1143, 170, 3513])).
% 1.43/1.65 tff(3515,plain,
% 1.43/1.65 (b(s(z), s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1133, 3514])).
% 1.43/1.65 tff(3516,plain,
% 1.43/1.65 (b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3515, 1781])).
% 1.43/1.65 tff(3517,plain,
% 1.43/1.65 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[58])).
% 1.43/1.65 tff(3518,plain,
% 1.43/1.65 (b(s(s(s(s(elem!1)))), z)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[2824, 1964])).
% 1.43/1.65 tff(3519,assumption,(~b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.43/1.65 tff(3520,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3519, 3518])).
% 1.43/1.65 tff(3521,plain,((~(z = elem!1)) | b(s(s(s(s(elem!1)))), z) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3522,plain,
% 1.43/1.65 (b(s(s(s(s(elem!1)))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3521, 58, 2824])).
% 1.43/1.65 tff(3523,assumption,(~b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.65 tff(3524,plain,
% 1.43/1.65 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2553, 1943, 1, 89, 90])).
% 1.43/1.65 tff(3525,plain,
% 1.43/1.65 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1252, 1958])).
% 1.43/1.65 tff(3526,plain,
% 1.43/1.65 (r(z, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1992, 3523])).
% 1.43/1.65 tff(3527,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3336, 141, 310, 407])).
% 1.43/1.65 tff(3528,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[37, 3527])).
% 1.43/1.65 tff(3529,plain,
% 1.43/1.65 (~r(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3358, 141, 310, 407])).
% 1.43/1.65 tff(3530,plain,
% 1.43/1.65 (b(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[197, 3529])).
% 1.43/1.65 tff(3531,plain,
% 1.43/1.65 (((~![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(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3532,plain,
% 1.43/1.65 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3533,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(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(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3532])).
% 1.43/1.65 tff(3534,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(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(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3533, 3531])).
% 1.43/1.65 tff(3535,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(3536,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3535, 3534])).
% 1.43/1.65 tff(3537,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3536, 141, 1368, 170, 407])).
% 1.43/1.65 tff(3538,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3539,plain,
% 1.43/1.65 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3538, 407, 170])).
% 1.43/1.65 tff(3540,plain,
% 1.43/1.65 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1432, 3539, 399])).
% 1.43/1.65 tff(3541,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[353, 349, 11])).
% 1.43/1.65 tff(3542,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3543,plain,
% 1.43/1.65 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3544,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3543])).
% 1.43/1.65 tff(3545,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3544, 3542])).
% 1.43/1.65 tff(3546,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(3547,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 1.43/1.65 tff(3548,plain,
% 1.43/1.65 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3547, 245, 235, 234, 288, 1943])).
% 1.43/1.65 tff(3549,plain,
% 1.43/1.65 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1263, 3548, 1])).
% 1.43/1.65 tff(3550,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2853, 3549, 3541, 96, 572, 2824, 2014, 1390])).
% 1.43/1.65 tff(3551,plain,((~b(s(elem!1), z)) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3552,plain,
% 1.43/1.65 (~b(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3551, 3540, 2824, 572, 1, 2338, 3530, 3528, 1943])).
% 1.43/1.65 tff(3553,plain,
% 1.43/1.65 (r(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[653, 32, 638, 3552])).
% 1.43/1.65 tff(3554,plain,
% 1.43/1.65 (~r(z, elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[649, 3553, 572])).
% 1.43/1.65 tff(3555,plain,
% 1.43/1.65 (z = elem!1),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[175, 3554, 90])).
% 1.43/1.65 tff(3556,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3555])).
% 1.43/1.65 tff(3557,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(symmetry,[status(thm)],[3556])).
% 1.43/1.65 tff(3558,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[170, 3557])).
% 1.43/1.65 tff(3559,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3527, 3558])).
% 1.43/1.65 tff(3560,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | b(z, elem!1) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3561,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3560, 3526, 90, 1277, 3524, 1, 1943, 170, 1951])).
% 1.43/1.65 tff(3562,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1239, 3561, 3525])).
% 1.43/1.65 tff(3563,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[575, 141, 1277, 170])).
% 1.43/1.65 tff(3564,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[353, 3563, 1958])).
% 1.43/1.65 tff(3565,plain,
% 1.43/1.65 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.65 tff(3566,plain,
% 1.43/1.65 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3565, 338])).
% 1.43/1.65 tff(3567,plain,
% 1.43/1.65 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3566])).
% 1.43/1.65 tff(3568,plain,
% 1.43/1.65 (~(elem!1 = s(z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[228, 3567])).
% 1.43/1.65 tff(3569,plain,
% 1.43/1.65 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.65 tff(3570,plain,
% 1.43/1.65 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.43/1.65 inference(symmetry,[status(thm)],[3569])).
% 1.43/1.65 tff(3571,plain,
% 1.43/1.65 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3100])).
% 1.43/1.65 tff(3572,plain,
% 1.43/1.65 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.43/1.65 inference(symmetry,[status(thm)],[3571])).
% 1.43/1.65 tff(3573,plain,
% 1.43/1.65 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.43/1.65 inference(transitivity,[status(thm)],[3572, 3570])).
% 1.43/1.65 tff(3574,plain,
% 1.43/1.65 (r(s(z), z)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1277, 3573])).
% 1.43/1.65 tff(3575,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(z, 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), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3576,plain,
% 1.43/1.65 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3577,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(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(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3576])).
% 1.43/1.65 tff(3578,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(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(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3577, 3575])).
% 1.43/1.65 tff(3579,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(3580,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 1.43/1.65 tff(3581,plain,
% 1.43/1.65 (~r(z, s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3580, 141, 3526, 1264])).
% 1.43/1.65 tff(3582,plain,
% 1.43/1.65 (b(z, s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[644, 3581])).
% 1.43/1.65 tff(3583,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(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), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3584,plain,
% 1.43/1.65 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3585,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(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), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3584])).
% 1.43/1.65 tff(3586,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(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), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3585, 3583])).
% 1.43/1.65 tff(3587,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(3588,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 1.43/1.65 tff(3589,plain,
% 1.43/1.65 (~r(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3588, 141, 3526, 1264])).
% 1.43/1.65 tff(3590,plain,
% 1.43/1.65 (b(s(elem!1), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[653, 32, 638, 3589])).
% 1.43/1.65 tff(3591,plain,
% 1.43/1.65 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2837, 1266, 1264])).
% 1.43/1.65 tff(3592,plain,
% 1.43/1.65 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1432, 3591, 399])).
% 1.43/1.65 tff(3593,plain,
% 1.43/1.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2853, 3592, 96, 1266, 2824, 2348, 1264])).
% 1.43/1.65 tff(3594,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[353, 3593, 2338])).
% 1.43/1.65 tff(3595,plain,
% 1.43/1.65 (~b(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2861, 245, 3594, 3590, 3582])).
% 1.43/1.65 tff(3596,plain,
% 1.43/1.65 (r(z, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[197, 3595])).
% 1.43/1.65 tff(3597,plain,
% 1.43/1.65 (~b(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2871, 245, 3594, 3590, 3582])).
% 1.43/1.65 tff(3598,plain,
% 1.43/1.65 (r(s(s(s(elem!1))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[37, 3597])).
% 1.43/1.65 tff(3599,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.43/1.65 tff(3600,plain,
% 1.43/1.65 (~(elem!1 = s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1672, 102])).
% 1.43/1.65 tff(3601,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3602,plain,
% 1.43/1.65 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3603,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3602])).
% 1.43/1.65 tff(3604,plain,
% 1.43/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3603, 3601])).
% 1.43/1.65 tff(3605,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(3606,plain,
% 1.43/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3605, 3604])).
% 1.43/1.65 tff(3607,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3606, 141, 131, 2070, 2069])).
% 1.43/1.65 tff(3608,plain,((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3609,plain,
% 1.43/1.65 (~r(elem!1, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3608, 131, 2069])).
% 1.43/1.65 tff(3610,plain,
% 1.43/1.65 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1724, 3609, 3600])).
% 1.43/1.65 tff(3611,plain,
% 1.43/1.65 (~r(s(z), s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[2109, 1355, 220])).
% 1.43/1.65 tff(3612,plain,
% 1.43/1.65 (b(s(z), s(s(s(elem!1))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1133, 3611])).
% 1.43/1.65 tff(3613,plain,
% 1.43/1.65 (b(elem!1, s(z))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[281, 2100, 3599])).
% 1.43/1.65 tff(3614,plain,
% 1.43/1.65 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[110, 2112, 102])).
% 1.43/1.65 tff(3615,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.65 tff(3616,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3617,plain,
% 1.43/1.65 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(3618,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3617])).
% 1.43/1.65 tff(3619,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[3618, 3616])).
% 1.43/1.65 tff(3620,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(3621,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 1.43/1.65 tff(3622,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3621, 245, 1390, 301, 1427, 3615, 2101])).
% 1.43/1.65 tff(3623,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3624,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3623, 3614, 3613, 3612, 3610, 1390])).
% 1.43/1.65 tff(3625,plain,((~r(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = elem!1) | (elem!1 = s(z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(3626,plain,
% 1.43/1.65 (~r(elem!1, z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[3625, 3592, 96, 3599, 3598, 220, 3596])).
% 1.43/1.65 tff(3627,plain,
% 1.43/1.65 (elem!1 = z),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[128, 3626, 89])).
% 1.43/1.65 tff(3628,plain,
% 1.43/1.65 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3627])).
% 1.43/1.65 tff(3629,plain,
% 1.43/1.65 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[3628])).
% 1.43/1.65 tff(3630,plain,
% 1.43/1.65 ((~b(z, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[3629])).
% 1.43/1.66 tff(3631,plain,
% 1.43/1.66 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3523, 3630])).
% 1.43/1.66 tff(3632,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3592, 3631])).
% 1.43/1.66 tff(3633,plain,((s(elem!1) = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | b(elem!1, z) | (elem!1 = s(z)) | (~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | b(s(elem!1), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3634,plain,
% 1.43/1.66 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3633, 3574, 1, 2824, 3523, 89, 1951, 564, 3568])).
% 1.43/1.66 tff(3635,plain,
% 1.43/1.66 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1295, 3634, 1276, 3564])).
% 1.43/1.66 tff(3636,plain,
% 1.43/1.66 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[420, 3635, 7])).
% 1.43/1.66 tff(3637,plain,
% 1.43/1.66 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.66 tff(3638,plain,
% 1.43/1.66 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3526, 3637])).
% 1.43/1.66 tff(3639,plain,
% 1.43/1.66 ((z = elem!1) <=> (elem!1 = z)),
% 1.43/1.66 inference(symmetry,[status(thm)],[119])).
% 1.43/1.66 tff(3640,plain,
% 1.43/1.66 (elem!1 = z),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[114, 3639])).
% 1.43/1.66 tff(3641,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.43/1.66 tff(3642,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3641, 3640])).
% 1.43/1.66 tff(3643,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3644,plain,
% 1.43/1.66 (elem!1 = z),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3643, 114])).
% 1.43/1.66 tff(3645,plain,
% 1.43/1.66 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.66 tff(3646,plain,
% 1.43/1.66 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.43/1.66 inference(symmetry,[status(thm)],[3645])).
% 1.43/1.66 tff(3647,plain,
% 1.43/1.66 (r(s(elem!1), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1277, 3646])).
% 1.43/1.66 tff(3648,plain,
% 1.43/1.66 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3538, 170, 1368])).
% 1.43/1.66 tff(3649,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1239, 3648, 2014])).
% 1.43/1.66 tff(3650,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.43/1.66 inference(monotonicity,[status(thm)],[120])).
% 1.43/1.66 tff(3651,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[170, 3650])).
% 1.43/1.66 tff(3652,plain,
% 1.43/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3653,plain,
% 1.43/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(3654,plain,
% 1.43/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3653, 3652])).
% 1.43/1.66 tff(3655,plain,
% 1.43/1.66 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3654, 141, 1097, 3651])).
% 1.43/1.66 tff(3656,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[353, 3655, 11])).
% 1.43/1.66 tff(3657,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3658,plain,
% 1.43/1.66 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3659,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[3658])).
% 1.43/1.66 tff(3660,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[3659, 3657])).
% 1.43/1.66 tff(3661,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(3662,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3661, 3660])).
% 1.43/1.66 tff(3663,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3662, 245, 3656, 838, 556, 3649, 1943])).
% 1.43/1.66 tff(3664,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), z)) | (~(elem!1 = z)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3665,plain,
% 1.43/1.66 (~b(z, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3664, 3634, 170, 1943, 1958, 3647, 3644, 3638])).
% 1.43/1.66 tff(3666,plain,
% 1.43/1.66 (r(z, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[644, 3665])).
% 1.43/1.66 tff(3667,plain,
% 1.43/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(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(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3668,plain,
% 1.43/1.66 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3669,plain,
% 1.43/1.66 (((~![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(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[3668])).
% 1.43/1.66 tff(3670,plain,
% 1.43/1.66 (((~![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(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[3669, 3667])).
% 1.43/1.66 tff(3671,plain,
% 1.43/1.66 ((~![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(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(3672,plain,
% 1.43/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3671, 3670])).
% 1.43/1.66 tff(3673,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3672, 141, 1342, 310, 406])).
% 1.43/1.66 tff(3674,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3675,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3674, 3666, 3636, 3526])).
% 1.43/1.66 tff(3676,plain,((~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | b(z, s(s(s(s(elem!1))))) | b(elem!1, z) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3677,plain,
% 1.43/1.66 (~(z = elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3676, 3562, 1943, 170, 1, 3524, 3523, 89, 564])).
% 1.43/1.66 tff(3678,plain,
% 1.43/1.66 (r(z, elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[175, 3677, 90])).
% 1.43/1.66 tff(3679,plain,
% 1.43/1.66 (~r(s(s(s(elem!1))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[179, 141, 3678, 170])).
% 1.43/1.66 tff(3680,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[37, 3679])).
% 1.43/1.66 tff(3681,plain,
% 1.43/1.66 (((~![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(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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3682,plain,
% 1.43/1.66 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3683,plain,
% 1.43/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(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(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[3682])).
% 1.43/1.66 tff(3684,plain,
% 1.43/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(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(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[3683, 3681])).
% 1.43/1.66 tff(3685,plain,
% 1.43/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(3686,plain,
% 1.43/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3685, 3684])).
% 1.43/1.66 tff(3687,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3686, 141, 289, 1368, 310])).
% 1.43/1.66 tff(3688,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3689,plain,
% 1.43/1.66 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3688, 3678, 3526])).
% 1.43/1.66 tff(3690,plain,
% 1.43/1.66 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1432, 3689, 1951])).
% 1.43/1.66 tff(3691,plain,
% 1.43/1.66 (~r(s(elem!1), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[649, 3678, 1277])).
% 1.43/1.66 tff(3692,plain,
% 1.43/1.66 (b(s(elem!1), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[653, 32, 638, 3691])).
% 1.43/1.66 tff(3693,plain,
% 1.43/1.66 (~r(z, s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[187, 141, 3678, 170])).
% 1.43/1.66 tff(3694,plain,
% 1.43/1.66 (b(z, s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[197, 3693])).
% 1.43/1.66 tff(3695,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3551, 3694, 3692, 3524, 1277, 1, 1958, 3690, 3680, 1943])).
% 1.43/1.66 tff(3696,plain,(b(z, s(s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), elem!1)) | b(z, elem!1) | b(elem!1, z) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3697,plain,
% 1.43/1.66 (b(z, s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3696, 170, 90, 564, 3522, 84, 1])).
% 1.43/1.66 tff(3698,plain,
% 1.43/1.66 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3697, 3517])).
% 1.43/1.66 tff(3699,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3700,plain,
% 1.43/1.66 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3701,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[3700])).
% 1.43/1.66 tff(3702,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[3701, 3699])).
% 1.43/1.66 tff(3703,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(3704,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 1.43/1.66 tff(3705,plain,
% 1.43/1.66 (~b(elem!1, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3704, 245, 3698, 2824, 556])).
% 1.43/1.66 tff(3706,plain,
% 1.43/1.66 (r(elem!1, s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2777, 3705, 2563])).
% 1.43/1.66 tff(3707,plain,
% 1.43/1.66 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3236, 3706, 2824, 39, 1490, 3698, 1572, 3512, 3516, 332])).
% 1.43/1.66 tff(3708,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[420, 3707, 7])).
% 1.43/1.66 tff(3709,plain,
% 1.43/1.66 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1295, 3708, 556, 3512])).
% 1.43/1.66 tff(3710,plain,
% 1.43/1.66 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1239, 3709, 1304])).
% 1.43/1.66 tff(3711,plain,
% 1.43/1.66 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3089, 3512, 170, 39, 1277])).
% 1.43/1.66 tff(3712,assumption,(~r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.43/1.66 tff(3713,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3712, 2629])).
% 1.43/1.66 tff(3714,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(elem!1))))), elem!1) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(3715,plain,
% 1.43/1.66 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3714, 3711, 39])).
% 1.43/1.66 tff(3716,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[787, 3715, 3029])).
% 1.43/1.66 tff(3717,plain,
% 1.43/1.66 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3716, 3026])).
% 1.43/1.66 tff(3718,plain,
% 1.43/1.66 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3043, 245, 3698, 2824, 3717])).
% 1.43/1.66 tff(3719,plain,
% 1.43/1.66 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1526, 32, 3718, 1490])).
% 1.43/1.66 tff(3720,plain,
% 1.43/1.66 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3291, 141, 3710, 3719])).
% 1.43/1.66 tff(3721,plain,
% 1.43/1.66 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3720, 1834])).
% 1.43/1.66 tff(3722,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[909, 3721])).
% 1.43/1.66 tff(3723,plain,
% 1.43/1.66 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3722, 1833])).
% 1.43/1.66 tff(3724,plain,
% 1.43/1.66 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3725,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[3724])).
% 1.43/1.66 tff(3726,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[3725, 3200])).
% 1.43/1.66 tff(3727,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(3728,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3727, 3726])).
% 1.43/1.66 tff(3729,plain,
% 1.43/1.66 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3728, 245, 3512, 3516, 3723])).
% 1.43/1.66 tff(3730,plain,
% 1.43/1.66 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3059, 3729, 3066])).
% 1.43/1.66 tff(3731,plain,
% 1.43/1.66 (((~![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(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(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3732,plain,
% 1.43/1.66 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3733,plain,
% 1.43/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, 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(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[3732])).
% 1.43/1.66 tff(3734,plain,
% 1.43/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, 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(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[3733, 3731])).
% 1.43/1.66 tff(3735,plain,
% 1.43/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(3736,plain,
% 1.43/1.66 ((~![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(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 1.43/1.66 tff(3737,plain,
% 1.43/1.66 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3736, 141, 3706, 3730])).
% 1.43/1.66 tff(3738,plain,
% 1.43/1.66 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3737, 1654])).
% 1.43/1.66 tff(3739,plain,
% 1.43/1.66 (b(elem!1, s(s(s(s(s(z))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[720, 3738, 1652])).
% 1.43/1.66 tff(3740,plain,
% 1.43/1.66 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3739, 1648])).
% 1.43/1.66 tff(3741,plain,
% 1.43/1.66 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[3252, 141, 3710, 3719])).
% 1.43/1.66 tff(3742,plain,
% 1.43/1.66 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3741, 1500])).
% 1.43/1.66 tff(3743,plain,
% 1.43/1.66 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1515, 3742])).
% 1.43/1.66 tff(3744,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[3743, 1498])).
% 1.43/1.66 tff(3745,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3746,plain,
% 1.43/1.66 (((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(3747,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[3746])).
% 1.43/1.66 tff(3748,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[3747, 3745])).
% 1.43/1.66 tff(3749,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(3750,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3749, 3748])).
% 1.43/1.67 tff(3751,plain,
% 1.43/1.67 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3750, 245, 3717, 3744, 3740])).
% 1.43/1.67 tff(3752,plain,
% 1.43/1.67 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1724, 3751, 1673])).
% 1.43/1.67 tff(3753,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.67 tff(3754,plain,
% 1.43/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3755,plain,
% 1.43/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(3756,plain,
% 1.43/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3755, 3754])).
% 1.43/1.67 tff(3757,plain,
% 1.43/1.67 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3756, 141, 2070])).
% 1.43/1.67 tff(3758,plain,
% 1.43/1.67 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3757, 3753])).
% 1.43/1.67 tff(3759,plain,
% 1.43/1.67 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1768, 3758, 1855])).
% 1.43/1.67 tff(3760,plain,
% 1.43/1.67 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3170, 245, 1390, 2824, 3759])).
% 1.43/1.67 tff(3761,plain,
% 1.43/1.67 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[501, 3760, 2193])).
% 1.43/1.67 tff(3762,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2928, 141, 407, 3761, 3753])).
% 1.43/1.67 tff(3763,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3764,plain,
% 1.43/1.67 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3763, 3752, 332, 2824, 3710, 1555, 3698])).
% 1.43/1.67 tff(3765,plain,
% 1.43/1.67 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[1617])).
% 1.43/1.67 tff(3766,plain,
% 1.43/1.67 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[1615])).
% 1.43/1.67 tff(3767,plain,
% 1.43/1.67 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3766])).
% 1.43/1.67 tff(3768,assumption,(~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.67 tff(3769,plain,
% 1.43/1.67 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3768, 3767])).
% 1.43/1.67 tff(3770,plain,
% 1.43/1.67 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1630, 3769, 1616])).
% 1.43/1.67 tff(3771,plain,
% 1.43/1.67 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3770, 3765])).
% 1.43/1.67 tff(3772,assumption,(~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))), introduced(assumption)).
% 1.43/1.67 tff(3773,plain,
% 1.43/1.67 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3772, 1780])).
% 1.43/1.67 tff(3774,plain,
% 1.43/1.67 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1820, 3773])).
% 1.43/1.67 tff(3775,plain,
% 1.43/1.67 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3774, 1544])).
% 1.43/1.67 tff(3776,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3185, 245, 1287, 2939, 3775, 3771])).
% 1.43/1.67 tff(3777,plain,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3778,plain,
% 1.43/1.67 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3777, 3764, 3516, 39, 1572, 3512])).
% 1.43/1.67 tff(3779,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3780,plain,
% 1.43/1.67 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3781,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3780])).
% 1.43/1.67 tff(3782,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3781, 3779])).
% 1.43/1.67 tff(3783,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(3784,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3783, 3782])).
% 1.43/1.67 tff(3785,plain,
% 1.43/1.67 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3784, 245, 1390, 2824, 2718, 1543])).
% 1.43/1.67 tff(3786,plain,
% 1.43/1.67 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1607, 32, 1542, 3785])).
% 1.43/1.67 tff(3787,plain,
% 1.43/1.67 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3170, 245, 1390, 2824, 2718])).
% 1.43/1.67 tff(3788,plain,
% 1.43/1.67 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[501, 3787, 2193])).
% 1.43/1.67 tff(3789,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1852, 141, 3788, 1849, 3786])).
% 1.43/1.67 tff(3790,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(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))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3791,plain,
% 1.43/1.67 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3790, 3719, 2692, 332, 3698, 2824, 3717])).
% 1.43/1.67 tff(3792,plain,
% 1.43/1.67 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1768, 3791, 1555])).
% 1.43/1.67 tff(3793,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2710, 141, 1277, 3792, 3778])).
% 1.43/1.67 tff(3794,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1)) | b(z, elem!1) | b(s(elem!1), elem!1) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3795,plain,
% 1.43/1.67 (~r(s(s(s(elem!1))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3794, 2823, 3501, 3296, 2569, 90, 564, 1])).
% 1.43/1.67 tff(3796,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[110, 3795, 96])).
% 1.43/1.67 tff(3797,plain,
% 1.43/1.67 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3505])).
% 1.43/1.67 tff(3798,plain,
% 1.43/1.67 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1571, 3501, 1])).
% 1.43/1.67 tff(3799,plain,
% 1.43/1.67 ((~b(s(s(s(s(s(elem!1))))), elem!1)) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3025])).
% 1.43/1.67 tff(3800,plain,
% 1.43/1.67 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[58])).
% 1.43/1.67 tff(3801,plain,
% 1.43/1.67 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.43/1.67 inference(symmetry,[status(thm)],[3800])).
% 1.43/1.67 tff(3802,plain,
% 1.43/1.67 (r(s(elem!1), z)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[572, 3801])).
% 1.43/1.67 tff(3803,plain,
% 1.43/1.67 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3100])).
% 1.43/1.67 tff(3804,plain,
% 1.43/1.67 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.67 tff(3805,plain,
% 1.43/1.67 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3804, 3803])).
% 1.43/1.67 tff(3806,plain,
% 1.43/1.67 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.67 tff(3807,plain,
% 1.43/1.67 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.43/1.67 inference(symmetry,[status(thm)],[3806])).
% 1.43/1.67 tff(3808,plain,
% 1.43/1.67 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3100])).
% 1.43/1.67 tff(3809,plain,
% 1.43/1.67 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.43/1.67 inference(symmetry,[status(thm)],[3808])).
% 1.43/1.67 tff(3810,plain,
% 1.43/1.67 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3809, 3807])).
% 1.43/1.67 tff(3811,plain,
% 1.43/1.67 ((~r(elem!1, s(elem!1))) <=> (~r(z, s(z)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3810])).
% 1.43/1.67 tff(3812,plain,
% 1.43/1.67 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.43/1.67 inference(commutativity,[status(thm)],[])).
% 1.43/1.67 tff(3813,plain,
% 1.43/1.67 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[3812])).
% 1.43/1.67 tff(3814,plain,
% 1.43/1.67 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.67 tff(3815,plain,
% 1.43/1.67 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3814, 3813])).
% 1.43/1.67 tff(3816,plain,
% 1.43/1.67 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3815])).
% 1.43/1.67 tff(3817,plain,
% 1.43/1.67 (~(elem!1 = s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[22, 3816])).
% 1.43/1.67 tff(3818,plain,
% 1.43/1.67 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3318, 2824, 1427, 1276])).
% 1.43/1.67 tff(3819,plain,
% 1.43/1.67 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1724, 3818, 3817])).
% 1.43/1.67 tff(3820,plain,
% 1.43/1.67 (~r(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2762, 3819, 371])).
% 1.43/1.67 tff(3821,plain,
% 1.43/1.67 (~r(z, s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3820, 3811])).
% 1.43/1.67 tff(3822,plain,
% 1.43/1.67 (b(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1420, 3821, 1416])).
% 1.43/1.67 tff(3823,plain,
% 1.43/1.67 (b(elem!1, s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3822, 3805])).
% 1.43/1.67 tff(3824,plain,
% 1.43/1.67 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.67 tff(3825,plain,
% 1.43/1.67 ((~(s(elem!1) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3824])).
% 1.43/1.67 tff(3826,plain,
% 1.43/1.67 (~(s(elem!1) = elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[638, 3825])).
% 1.43/1.67 tff(3827,plain,
% 1.43/1.67 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.67 tff(3828,plain,
% 1.43/1.67 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3827, 61])).
% 1.43/1.67 tff(3829,plain,
% 1.43/1.67 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3828])).
% 1.43/1.67 tff(3830,plain,
% 1.43/1.67 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[66, 3829])).
% 1.43/1.67 tff(3831,plain,
% 1.43/1.67 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2849, 2824, 1427, 1276])).
% 1.43/1.67 tff(3832,plain,
% 1.43/1.67 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1432, 3831, 3830])).
% 1.43/1.67 tff(3833,plain,
% 1.43/1.67 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3814])).
% 1.43/1.67 tff(3834,plain,
% 1.43/1.67 (~(s(s(s(elem!1))) = elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[22, 3833])).
% 1.43/1.67 tff(3835,assumption,(s(elem!1) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.67 tff(3836,plain,
% 1.43/1.67 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3835])).
% 1.43/1.67 tff(3837,plain,
% 1.43/1.67 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.43/1.67 inference(symmetry,[status(thm)],[3836])).
% 1.43/1.67 tff(3838,plain,
% 1.43/1.67 (s(s(s(elem!1))) = elem!1),
% 1.43/1.67 inference(transitivity,[status(thm)],[206, 3837, 49])).
% 1.43/1.67 tff(3839,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[102, 3838])).
% 1.43/1.67 tff(3840,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3841,plain,
% 1.43/1.67 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3840, 3834])).
% 1.43/1.67 tff(3842,plain,
% 1.43/1.67 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3482, 3823, 1427, 2824, 1276])).
% 1.43/1.67 tff(3843,plain,
% 1.43/1.67 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1263, 3842, 3841])).
% 1.43/1.67 tff(3844,plain,
% 1.43/1.67 (~r(s(elem!1), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2837, 3843, 3832])).
% 1.43/1.67 tff(3845,plain,
% 1.43/1.67 (b(s(elem!1), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[568, 32, 3844, 3826])).
% 1.43/1.67 tff(3846,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3847,plain,
% 1.43/1.67 (((~b(s(elem!1), elem!1)) | (~b(s(s(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(elem!1), elem!1)) | (~b(s(s(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))), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3848,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3847])).
% 1.43/1.67 tff(3849,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3848, 3846])).
% 1.43/1.67 tff(3850,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(3851,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3850, 3849])).
% 1.43/1.67 tff(3852,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3851, 245, 3845, 1427, 3823, 2824, 1276])).
% 1.43/1.67 tff(3853,plain,((~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)))))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3854,plain,
% 1.43/1.67 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3853, 371, 2824, 58, 1427])).
% 1.43/1.67 tff(3855,plain,
% 1.43/1.67 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1239, 3854, 1309])).
% 1.43/1.67 tff(3856,plain,
% 1.43/1.67 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[415, 3855, 371])).
% 1.43/1.67 tff(3857,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[420, 3856, 164])).
% 1.43/1.67 tff(3858,plain,
% 1.43/1.67 (elem!1 = z),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3643, 58])).
% 1.43/1.67 tff(3859,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3860,plain,
% 1.43/1.67 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3861,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3860])).
% 1.43/1.67 tff(3862,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3861, 3859])).
% 1.43/1.67 tff(3863,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(3864,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3863, 3862])).
% 1.43/1.67 tff(3865,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3864, 245, 1103, 2824, 556, 10])).
% 1.43/1.67 tff(3866,plain,((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3867,plain,
% 1.43/1.67 (~b(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3866, 3857, 2824, 556])).
% 1.43/1.67 tff(3868,plain,
% 1.43/1.67 (r(elem!1, s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2777, 3867, 2774])).
% 1.43/1.67 tff(3869,plain,
% 1.43/1.67 (~r(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2762, 3868, 371])).
% 1.43/1.67 tff(3870,plain,
% 1.43/1.67 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1724, 3869, 1717])).
% 1.43/1.67 tff(3871,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3872,plain,
% 1.43/1.67 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3873,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[3872])).
% 1.43/1.67 tff(3874,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[3873, 3871])).
% 1.43/1.67 tff(3875,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(3876,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 1.43/1.67 tff(3877,plain,
% 1.43/1.67 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3876, 245, 1427, 3870, 2824])).
% 1.43/1.67 tff(3878,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1320, 3877, 3067])).
% 1.43/1.67 tff(3879,plain,
% 1.43/1.67 (((~![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(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(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(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(3880,plain,
% 1.43/1.67 ((~![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(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(3881,plain,
% 1.43/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3880, 3879])).
% 1.43/1.67 tff(3882,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3881, 141, 2751, 529, 3753])).
% 1.43/1.67 tff(3883,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3884,plain,
% 1.43/1.67 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3883, 2925, 2751])).
% 1.43/1.67 tff(3885,plain,
% 1.43/1.67 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3884, 3767])).
% 1.43/1.67 tff(3886,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2745, 3885])).
% 1.43/1.67 tff(3887,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(3888,plain,
% 1.43/1.67 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3887, 3878, 1616, 39, 2193, 1427, 3870, 2824])).
% 1.43/1.67 tff(3889,plain,
% 1.43/1.67 (z = elem!1),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[123, 120])).
% 1.43/1.68 tff(3890,plain,
% 1.43/1.68 (s(z) = s(elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[117, 3889])).
% 1.43/1.68 tff(3891,plain,
% 1.43/1.68 (s(elem!1) = s(z)),
% 1.43/1.68 inference(symmetry,[status(thm)],[3890])).
% 1.43/1.68 tff(3892,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3891])).
% 1.43/1.68 tff(3893,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.68 inference(symmetry,[status(thm)],[3892])).
% 1.43/1.68 tff(3894,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3891])).
% 1.43/1.68 tff(3895,plain,
% 1.43/1.68 ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3894])).
% 1.43/1.68 tff(3896,plain,
% 1.43/1.68 (z = elem!1),
% 1.43/1.68 inference(symmetry,[status(thm)],[120])).
% 1.43/1.68 tff(3897,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3896])).
% 1.43/1.68 tff(3898,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.43/1.68 inference(symmetry,[status(thm)],[3897])).
% 1.43/1.68 tff(3899,plain,
% 1.43/1.68 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (z = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[120])).
% 1.43/1.68 tff(3900,plain,
% 1.43/1.68 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = z)),
% 1.43/1.68 inference(transitivity,[status(thm)],[3899, 3398])).
% 1.43/1.68 tff(3901,plain,
% 1.43/1.68 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[3900])).
% 1.43/1.68 tff(3902,plain,
% 1.43/1.68 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.43/1.68 inference(transitivity,[status(thm)],[3901, 1548])).
% 1.43/1.68 tff(3903,plain,
% 1.43/1.68 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3902])).
% 1.43/1.68 tff(3904,plain,
% 1.43/1.68 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1554, 3903])).
% 1.43/1.68 tff(3905,assumption,(~b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.43/1.68 tff(3906,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1768, 3905, 3904])).
% 1.43/1.68 tff(3907,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3906, 3898])).
% 1.43/1.68 tff(3908,plain,
% 1.43/1.68 (((~![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(s(s(elem!1)))))), z)) | (~r(s(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), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3909,plain,
% 1.43/1.68 ((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(3910,plain,
% 1.43/1.68 ((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3909, 3908])).
% 1.43/1.68 tff(3911,plain,
% 1.43/1.68 ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3910, 141, 1097])).
% 1.43/1.68 tff(3912,plain,
% 1.43/1.68 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3911, 3907])).
% 1.43/1.68 tff(3913,plain,
% 1.43/1.68 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3912, 3895])).
% 1.43/1.68 tff(3914,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1820, 3913])).
% 1.43/1.68 tff(3915,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3914, 3893])).
% 1.43/1.68 tff(3916,plain,
% 1.43/1.68 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3917,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3916])).
% 1.43/1.68 tff(3918,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[3917, 1895])).
% 1.43/1.68 tff(3919,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(3920,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3919, 3918])).
% 1.43/1.68 tff(3921,plain,
% 1.43/1.68 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3920, 245, 556, 10])).
% 1.43/1.68 tff(3922,plain,
% 1.43/1.68 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3921, 3915])).
% 1.43/1.68 tff(3923,plain,
% 1.43/1.68 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[537, 3907, 310])).
% 1.43/1.68 tff(3924,plain,
% 1.43/1.68 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[501, 3923, 3922])).
% 1.43/1.68 tff(3925,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3924, 120])).
% 1.43/1.68 tff(3926,plain,
% 1.43/1.68 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.68 inference(symmetry,[status(thm)],[3925])).
% 1.43/1.68 tff(3927,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1943, 3926])).
% 1.43/1.68 tff(3928,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3905, 3927])).
% 1.43/1.68 tff(3929,plain,(b(s(s(s(s(s(s(elem!1)))))), elem!1) | (~b(s(s(s(s(elem!1)))), z)) | (~(elem!1 = z)) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(3930,plain,
% 1.43/1.68 (~r(z, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3929, 3888, 556, 3858, 3522, 3857, 3802])).
% 1.43/1.68 tff(3931,plain,
% 1.43/1.68 (b(z, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1992, 3930])).
% 1.43/1.68 tff(3932,plain,
% 1.43/1.68 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3931, 3517])).
% 1.43/1.68 tff(3933,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), 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(X0, 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))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3934,plain,
% 1.43/1.68 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3935,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, 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))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3934])).
% 1.43/1.68 tff(3936,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, 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))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[3935, 3933])).
% 1.43/1.68 tff(3937,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(3938,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3937, 3936])).
% 1.43/1.68 tff(3939,plain,
% 1.43/1.68 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3938, 245, 1427, 2101, 1543])).
% 1.43/1.68 tff(3940,plain,
% 1.43/1.68 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3939, 1658])).
% 1.43/1.68 tff(3941,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[909, 3940])).
% 1.43/1.68 tff(3942,plain,
% 1.43/1.68 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3941, 1656])).
% 1.43/1.68 tff(3943,plain,
% 1.43/1.68 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2985, 2101, 1390, 1427])).
% 1.43/1.68 tff(3944,plain,
% 1.43/1.68 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1320, 3943, 1487])).
% 1.43/1.68 tff(3945,plain,
% 1.43/1.68 (((~![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)))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3946,plain,
% 1.43/1.68 ((~![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)))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(3947,plain,
% 1.43/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 1.43/1.68 tff(3948,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3947, 141, 3944, 1849])).
% 1.43/1.68 tff(3949,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3948, 3942])).
% 1.43/1.68 tff(3950,plain,((~b(elem!1, s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(3951,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3950, 1543, 39, 1427, 2101, 1487, 1390])).
% 1.43/1.68 tff(3952,plain,
% 1.43/1.68 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1489, 1487])).
% 1.43/1.68 tff(3953,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(s(s(elem!1))))), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3954,plain,
% 1.43/1.68 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3955,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(s(s(elem!1))))), elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3954])).
% 1.43/1.68 tff(3956,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(s(s(elem!1))))), elem!1)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[3955, 3953])).
% 1.43/1.68 tff(3957,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), 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)))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(3958,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3957, 3956])).
% 1.43/1.68 tff(3959,plain,
% 1.43/1.68 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3958, 245, 1427, 2101, 2824, 1543])).
% 1.43/1.68 tff(3960,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1526, 32, 3959, 3952, 3951])).
% 1.43/1.68 tff(3961,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(3962,plain,
% 1.43/1.68 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3961, 3870, 1427, 39, 3067, 3932, 2824])).
% 1.43/1.68 tff(3963,plain,
% 1.43/1.68 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3962, 3799])).
% 1.43/1.68 tff(3964,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[787, 3963, 3029])).
% 1.43/1.68 tff(3965,plain,
% 1.43/1.68 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3714, 3964, 39])).
% 1.43/1.68 tff(3966,plain,
% 1.43/1.68 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1768, 3888, 1555])).
% 1.43/1.68 tff(3967,plain,
% 1.43/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3968,plain,
% 1.43/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(3969,plain,
% 1.43/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 1.43/1.68 tff(3970,plain,
% 1.43/1.68 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3969, 141, 3966, 3965])).
% 1.43/1.68 tff(3971,plain,
% 1.43/1.68 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2690, 3068])).
% 1.43/1.68 tff(3972,plain,
% 1.43/1.68 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3971, 2680])).
% 1.43/1.68 tff(3973,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1607, 32, 3972, 3970])).
% 1.43/1.68 tff(3974,plain,
% 1.43/1.68 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2710, 141, 572, 3966])).
% 1.43/1.68 tff(3975,plain,
% 1.43/1.68 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3974, 1780])).
% 1.43/1.68 tff(3976,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1820, 3975])).
% 1.43/1.68 tff(3977,plain,
% 1.43/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3976, 1544])).
% 1.43/1.68 tff(3978,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3033, 3965, 572])).
% 1.43/1.68 tff(3979,plain,
% 1.43/1.68 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3059, 3978, 3066])).
% 1.43/1.68 tff(3980,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3981,plain,
% 1.43/1.68 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(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(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(3982,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3981])).
% 1.43/1.68 tff(3983,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[3982, 3980])).
% 1.43/1.68 tff(3984,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(3985,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[3984, 3983])).
% 1.43/1.68 tff(3986,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3985, 245, 556, 3857, 3979, 3977, 3973])).
% 1.43/1.68 tff(3987,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(3988,plain,
% 1.43/1.68 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3987, 3296, 1277, 3501, 3796, 2823, 3798, 2699, 1673, 2563, 7, 1304])).
% 1.43/1.68 tff(3989,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[353, 3988, 2569])).
% 1.43/1.68 tff(3990,plain,
% 1.43/1.68 (~b(elem!1, s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2798, 3989, 3296, 7, 2562, 3796, 1277])).
% 1.43/1.68 tff(3991,plain,
% 1.43/1.68 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[114])).
% 1.43/1.68 tff(3992,plain,
% 1.43/1.68 (b(elem!1, s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[838, 3991])).
% 1.43/1.68 tff(3993,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[426, 3992])).
% 1.43/1.68 tff(3994,plain,((~b(z, s(elem!1))) | b(elem!1, s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(3995,plain,
% 1.43/1.68 (~b(z, s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3994, 3990, 3505])).
% 1.43/1.68 tff(3996,plain,
% 1.43/1.68 (r(z, s(elem!1))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[644, 3995])).
% 1.43/1.68 tff(3997,plain,
% 1.43/1.68 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.43/1.68 inference(monotonicity,[status(thm)],[3505])).
% 1.43/1.68 tff(3998,plain,
% 1.43/1.68 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.43/1.68 inference(symmetry,[status(thm)],[3997])).
% 1.43/1.68 tff(3999,plain,
% 1.43/1.68 (r(s(elem!1), z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1277, 3998])).
% 1.43/1.68 tff(4000,plain,
% 1.43/1.68 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[58])).
% 1.43/1.69 tff(4001,plain,
% 1.43/1.69 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3674, 310, 1342])).
% 1.43/1.69 tff(4002,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[420, 4001, 164])).
% 1.43/1.69 tff(4003,plain,
% 1.43/1.69 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1295, 4002, 556, 1287])).
% 1.43/1.69 tff(4004,plain,
% 1.43/1.69 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1239, 4003, 1309])).
% 1.43/1.69 tff(4005,plain,
% 1.43/1.69 (~r(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3360, 4004, 310])).
% 1.43/1.69 tff(4006,plain,
% 1.43/1.69 (b(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[197, 4005])).
% 1.43/1.69 tff(4007,plain,
% 1.43/1.69 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4006, 4000])).
% 1.43/1.69 tff(4008,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3929, 4002, 556, 3858, 3522, 310, 1097])).
% 1.43/1.69 tff(4009,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4010,plain,
% 1.43/1.69 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(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(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), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4011,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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), s(s(s(s(elem!1))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4010])).
% 1.43/1.69 tff(4012,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4011, 4009])).
% 1.43/1.69 tff(4013,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4014,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4013, 4012])).
% 1.43/1.69 tff(4015,plain,
% 1.43/1.69 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4014, 245, 1287, 2824, 556])).
% 1.43/1.69 tff(4016,plain,
% 1.43/1.69 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4015, 4002])).
% 1.43/1.69 tff(4017,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1320, 4016, 3067])).
% 1.43/1.69 tff(4018,plain,
% 1.43/1.69 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3887, 4017, 1616, 39, 2193, 1427, 4008, 2824])).
% 1.43/1.69 tff(4019,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4018, 4007])).
% 1.43/1.69 tff(4020,plain,((~r(z, s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(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)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4021,plain,
% 1.43/1.69 (~r(z, s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4020, 3798, 3501, 2699, 3796, 2823, 1304, 3296, 3999, 3989, 7, 3996])).
% 1.43/1.69 tff(4022,plain,
% 1.43/1.69 (b(z, s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1992, 4021])).
% 1.43/1.69 tff(4023,plain,
% 1.43/1.69 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4022, 3797])).
% 1.43/1.69 tff(4024,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4025,plain,
% 1.43/1.69 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4026,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4025])).
% 1.43/1.69 tff(4027,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4026, 4024])).
% 1.43/1.69 tff(4028,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4029,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4028, 4027])).
% 1.43/1.69 tff(4030,plain,
% 1.43/1.69 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4029, 245, 4023, 3796, 2823])).
% 1.43/1.69 tff(4031,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1320, 4030, 1312])).
% 1.43/1.69 tff(4032,plain,
% 1.43/1.69 (((~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)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4033,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4032])).
% 1.43/1.69 tff(4034,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4033, 2842])).
% 1.43/1.69 tff(4035,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4036,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4035, 4034])).
% 1.43/1.69 tff(4037,plain,
% 1.43/1.69 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4036, 245, 4023, 3796, 2823])).
% 1.43/1.69 tff(4038,plain,
% 1.43/1.69 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1239, 4037, 1304])).
% 1.43/1.69 tff(4039,plain,
% 1.43/1.69 (s(s(z)) = s(s(elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[3501])).
% 1.43/1.69 tff(4040,plain,
% 1.43/1.69 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4039])).
% 1.43/1.69 tff(4041,plain,
% 1.43/1.69 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.43/1.69 inference(symmetry,[status(thm)],[4040])).
% 1.43/1.69 tff(4042,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4041])).
% 1.43/1.69 tff(4043,plain,
% 1.43/1.69 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4042])).
% 1.43/1.69 tff(4044,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.69 tff(4045,plain,
% 1.43/1.69 (b(s(elem!1), s(s(s(s(s(s(elem!1))))))) <=> b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[1556])).
% 1.43/1.69 tff(4046,plain,
% 1.43/1.69 (b(s(z), s(s(s(s(s(s(elem!1))))))) <=> b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[4045])).
% 1.43/1.69 tff(4047,plain,
% 1.43/1.69 (r(s(z), s(s(s(s(s(s(elem!1))))))) <=> r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[39])).
% 1.43/1.69 tff(4048,plain,
% 1.43/1.69 (r(s(elem!1), s(s(s(s(s(s(elem!1))))))) <=> r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[4047])).
% 1.43/1.69 tff(4049,plain,
% 1.43/1.69 ((~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) <=> (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4048])).
% 1.43/1.69 tff(4050,plain,
% 1.43/1.69 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2952, 141, 572, 2700])).
% 1.43/1.69 tff(4051,plain,
% 1.43/1.69 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4050, 4049])).
% 1.43/1.69 tff(4052,plain,
% 1.43/1.69 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[470, 4051])).
% 1.43/1.69 tff(4053,plain,
% 1.43/1.69 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4052, 4046])).
% 1.43/1.69 tff(4054,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2713, 1544])).
% 1.43/1.69 tff(4055,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4056,plain,
% 1.43/1.69 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4057,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4056])).
% 1.43/1.69 tff(4058,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4057, 4055])).
% 1.43/1.69 tff(4059,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4060,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4059, 4058])).
% 1.43/1.69 tff(4061,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4060, 245, 1287, 4054, 4044, 4053])).
% 1.43/1.69 tff(4062,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4063,plain,
% 1.43/1.69 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4062, 4044, 1287, 39, 572])).
% 1.43/1.69 tff(4064,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1768, 4063, 1555])).
% 1.43/1.69 tff(4065,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4066,plain,
% 1.43/1.69 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(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(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4067,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4066])).
% 1.43/1.69 tff(4068,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[4067, 4065])).
% 1.43/1.69 tff(4069,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(4070,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4069, 4068])).
% 1.43/1.69 tff(4071,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4070, 245, 1390, 1427, 2824, 4064, 4044])).
% 1.43/1.69 tff(4072,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4073,plain,
% 1.43/1.69 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4072, 4023, 3796, 2823, 3989, 3501, 1277])).
% 1.43/1.69 tff(4074,plain,
% 1.43/1.69 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4073, 4043])).
% 1.43/1.69 tff(4075,plain,
% 1.43/1.69 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1630, 4074, 3798])).
% 1.43/1.69 tff(4076,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))), introduced(assumption)).
% 1.43/1.69 tff(4077,plain,
% 1.43/1.69 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4076, 1615])).
% 1.43/1.69 tff(4078,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3768, 4077])).
% 1.43/1.69 tff(4079,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(4080,plain,
% 1.43/1.69 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4079, 4075, 3501])).
% 1.43/1.69 tff(4081,plain,
% 1.43/1.69 (~r(elem!1, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3763, 4080, 2699, 2823, 4023, 3510, 4038])).
% 1.43/1.69 tff(4082,plain,
% 1.43/1.69 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1724, 4081, 1673])).
% 1.43/1.69 tff(4083,plain,
% 1.43/1.69 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3887, 4082, 3798, 3501, 2699, 3796, 4031, 2823])).
% 1.43/1.69 tff(4084,plain,
% 1.43/1.69 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1768, 4083, 3510])).
% 1.43/1.69 tff(4085,plain,
% 1.43/1.69 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2710, 141, 1277, 4084])).
% 1.43/1.69 tff(4086,plain,
% 1.43/1.69 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[4085, 3504])).
% 1.43/1.69 tff(4087,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[3501])).
% 1.43/1.69 tff(4088,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.69 inference(symmetry,[status(thm)],[4087])).
% 1.43/1.69 tff(4089,plain,
% 1.43/1.69 ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4088])).
% 1.43/1.69 tff(4090,plain,
% 1.43/1.69 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[3883, 4080, 4031])).
% 1.43/1.69 tff(4091,plain,
% 1.43/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[501, 4090, 2699])).
% 1.43/1.69 tff(4092,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4093,plain,
% 1.43/1.69 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(4094,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4093])).
% 1.43/1.69 tff(4095,plain,
% 1.43/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.70 inference(transitivity,[status(thm)],[4094, 4092])).
% 1.43/1.70 tff(4096,plain,
% 1.43/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.43/1.70 inference(quant_inst,[status(thm)],[])).
% 1.43/1.70 tff(4097,plain,
% 1.43/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[4096, 4095])).
% 1.43/1.70 tff(4098,plain,
% 1.43/1.70 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4097, 245, 4023, 2823, 3296, 4091])).
% 1.43/1.70 tff(4099,plain,
% 1.43/1.70 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[4098, 4089])).
% 1.43/1.70 tff(4100,plain,
% 1.43/1.70 ($false),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1820, 4099, 4086])).
% 1.43/1.70 tff(4101,plain,(b(z, elem!1) | (s(s(s(s(elem!1)))) = elem!1) | b(s(elem!1), elem!1) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.70 tff(4102,plain,
% 1.43/1.70 (b(z, elem!1)),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[4101, 2562, 564, 1])).
% 1.43/1.70 tff(4103,plain,
% 1.43/1.70 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1284, 130, 572])).
% 1.43/1.70 tff(4104,plain,
% 1.43/1.70 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[420, 4103, 7])).
% 1.43/1.70 tff(4105,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.43/1.70 tff(4106,plain,
% 1.43/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(4107,plain,
% 1.43/1.70 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(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)))))))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(4108,plain,
% 1.43/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4107])).
% 1.53/1.70 tff(4109,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4108, 4106])).
% 1.53/1.70 tff(4110,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4111,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4110, 4109])).
% 1.53/1.70 tff(4112,plain,
% 1.53/1.70 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4111, 245, 556, 1276, 4104])).
% 1.53/1.70 tff(4113,plain,
% 1.53/1.70 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2091, 32, 4112])).
% 1.53/1.70 tff(4114,plain,
% 1.53/1.70 (r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4113, 2081])).
% 1.53/1.70 tff(4115,plain,
% 1.53/1.70 (~r(elem!1, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2762, 2070, 371])).
% 1.53/1.70 tff(4116,plain,
% 1.53/1.70 (b(elem!1, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2777, 4115, 2774])).
% 1.53/1.70 tff(4117,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(z, 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(X0, 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(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4118,plain,
% 1.53/1.70 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4119,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4118])).
% 1.53/1.70 tff(4120,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4119, 4117])).
% 1.53/1.70 tff(4121,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4122,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4121, 4120])).
% 1.53/1.70 tff(4123,plain,
% 1.53/1.70 (~b(s(s(s(elem!1))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4122, 245, 4105, 1427, 4116, 556, 1276])).
% 1.53/1.70 tff(4124,plain,
% 1.53/1.70 (r(s(s(s(elem!1))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[37, 4123])).
% 1.53/1.70 tff(4125,plain,
% 1.53/1.70 (((~![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))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4126,plain,
% 1.53/1.70 ((~![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))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4127,plain,
% 1.53/1.70 ((~![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)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4126, 4125])).
% 1.53/1.70 tff(4128,plain,
% 1.53/1.70 ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4127, 141])).
% 1.53/1.70 tff(4129,plain,
% 1.53/1.70 (~r(elem!1, z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4128, 4124, 2070])).
% 1.53/1.70 tff(4130,plain,
% 1.53/1.70 (b(elem!1, z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[128, 4129, 3641])).
% 1.53/1.70 tff(4131,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4132,plain,
% 1.53/1.70 (((~b(z, elem!1)) | (~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(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4133,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4132])).
% 1.53/1.70 tff(4134,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4133, 4131])).
% 1.53/1.70 tff(4135,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4136,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4135, 4134])).
% 1.53/1.70 tff(4137,plain,
% 1.53/1.70 (~b(z, s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4136, 245, 4105, 4130, 1427])).
% 1.53/1.70 tff(4138,plain,
% 1.53/1.70 (r(z, s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[197, 4137])).
% 1.53/1.70 tff(4139,plain,
% 1.53/1.70 (~r(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2303, 141, 4138, 2133])).
% 1.53/1.70 tff(4140,plain,
% 1.53/1.70 (b(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[644, 4139])).
% 1.53/1.70 tff(4141,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4142,plain,
% 1.53/1.70 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4143,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4142])).
% 1.53/1.70 tff(4144,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4143, 4141])).
% 1.53/1.70 tff(4145,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4146,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4145, 4144])).
% 1.53/1.70 tff(4147,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4146, 245, 4130, 4116, 4140, 556, 10])).
% 1.53/1.70 tff(4148,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (elem!1 = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(4149,plain,
% 1.53/1.70 (~r(elem!1, s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4148, 4114, 4104, 556, 4105, 1427, 3641, 1276, 2563, 371])).
% 1.53/1.70 tff(4150,plain,
% 1.53/1.70 (b(elem!1, s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1724, 4149, 1673])).
% 1.53/1.70 tff(4151,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4152,plain,
% 1.53/1.70 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4153,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4152])).
% 1.53/1.70 tff(4154,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4153, 4151])).
% 1.53/1.70 tff(4155,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(4156,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[4155, 4154])).
% 1.53/1.70 tff(4157,plain,
% 1.53/1.70 (~b(z, s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[4156, 245, 4105, 1427, 4150])).
% 1.53/1.70 tff(4158,plain,
% 1.53/1.70 (r(z, s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[197, 4157])).
% 1.53/1.70 tff(4159,plain,
% 1.53/1.70 (~r(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2303, 141, 4158, 4114])).
% 1.53/1.70 tff(4160,plain,
% 1.53/1.70 (b(z, s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[644, 4159])).
% 1.53/1.70 tff(4161,plain,
% 1.53/1.70 (~r(s(elem!1), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2551, 141, 4158, 4114])).
% 1.53/1.70 tff(4162,plain,
% 1.53/1.70 (b(s(elem!1), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1039, 4161])).
% 1.53/1.70 tff(4163,plain,
% 1.53/1.70 (~b(s(s(s(s(elem!1)))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[3304, 4162, 556, 4160])).
% 1.53/1.70 tff(4164,plain,
% 1.53/1.70 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2558, 4163])).
% 1.53/1.70 tff(4165,plain,
% 1.53/1.70 (~r(elem!1, z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[146, 4164, 130])).
% 1.53/1.70 tff(4166,plain,
% 1.53/1.70 (b(elem!1, z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[128, 4165, 3641])).
% 1.53/1.70 tff(4167,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4168,plain,
% 1.53/1.70 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(4169,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[4168])).
% 1.53/1.70 tff(4170,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[4169, 4167])).
% 1.53/1.70 tff(4171,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4172,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4171, 4170])).
% 1.53/1.71 tff(4173,plain,
% 1.53/1.71 (~b(s(s(s(elem!1))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4172, 245, 4105, 1427, 4150])).
% 1.53/1.71 tff(4174,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[37, 4173])).
% 1.53/1.71 tff(4175,plain,
% 1.53/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4176,plain,
% 1.53/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4177,plain,
% 1.53/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4176, 4175])).
% 1.53/1.71 tff(4178,plain,
% 1.53/1.71 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4177, 141, 4174, 4164])).
% 1.53/1.71 tff(4179,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1320, 4178, 1312])).
% 1.53/1.71 tff(4180,plain,
% 1.53/1.71 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[225, 220, 106])).
% 1.53/1.71 tff(4181,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[217, 4180])).
% 1.53/1.71 tff(4182,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2189, 245, 1427, 2111, 2101, 1528, 4181])).
% 1.53/1.71 tff(4183,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4184,plain,
% 1.53/1.71 (~r(s(z), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4183, 4179, 4150, 4174, 1427, 4164])).
% 1.53/1.71 tff(4185,plain,
% 1.53/1.71 (b(s(z), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[232, 4184])).
% 1.53/1.71 tff(4186,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.53/1.71 tff(4187,assumption,(b(z, s(z))), introduced(assumption)).
% 1.53/1.71 tff(4188,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.53/1.71 tff(4189,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4190,plain,
% 1.53/1.71 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4191,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4190])).
% 1.53/1.71 tff(4192,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[4191, 4189])).
% 1.53/1.71 tff(4193,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4194,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4193, 4192])).
% 1.53/1.71 tff(4195,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4194, 245, 4105, 355, 4188, 838, 4187])).
% 1.53/1.71 tff(4196,plain,((~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4197,plain,
% 1.53/1.71 (~b(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4196, 355, 4105, 838, 4187])).
% 1.53/1.71 tff(4198,plain,
% 1.53/1.71 (r(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[369, 4197, 358])).
% 1.53/1.71 tff(4199,plain,
% 1.53/1.71 (((~![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(z))) | (~r(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(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4200,plain,
% 1.53/1.71 (((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4201,plain,
% 1.53/1.71 (((~![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(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4200])).
% 1.53/1.71 tff(4202,plain,
% 1.53/1.71 (((~![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(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[4201, 4199])).
% 1.53/1.71 tff(4203,plain,
% 1.53/1.71 ((~![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)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4204,plain,
% 1.53/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4203, 4202])).
% 1.53/1.71 tff(4205,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4204, 141, 572, 268, 998])).
% 1.53/1.71 tff(4206,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4207,plain,
% 1.53/1.71 (~r(elem!1, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4206, 4198, 572])).
% 1.53/1.71 tff(4208,plain,
% 1.53/1.71 (b(elem!1, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[281, 4207, 3599])).
% 1.53/1.71 tff(4209,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4210,plain,
% 1.53/1.71 (((~b(elem!1, z)) | (~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(s(z), z)) | (~b(elem!1, s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4211,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(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(X0, 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, s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4210])).
% 1.53/1.71 tff(4212,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(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(X0, 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, s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[4211, 4209])).
% 1.53/1.71 tff(4213,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4214,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4213, 4212])).
% 1.53/1.71 tff(4215,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4214, 245, 4105, 4186, 4208, 355])).
% 1.53/1.71 tff(4216,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~b(z, s(elem!1))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4217,plain,
% 1.53/1.71 (~b(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4216, 355, 4105, 838, 4186, 358, 572, 3599])).
% 1.53/1.71 tff(4218,plain,
% 1.53/1.71 (r(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1421, 4217])).
% 1.53/1.71 tff(4219,plain,
% 1.53/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4220,plain,
% 1.53/1.71 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4221,plain,
% 1.53/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4220])).
% 1.53/1.71 tff(4222,plain,
% 1.53/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[4221, 4219])).
% 1.53/1.71 tff(4223,plain,
% 1.53/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4224,plain,
% 1.53/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4223, 4222])).
% 1.53/1.71 tff(4225,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4224, 141, 106, 1449, 219])).
% 1.53/1.71 tff(4226,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4227,plain,
% 1.53/1.71 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4226, 4218, 106])).
% 1.53/1.71 tff(4228,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[217, 4227])).
% 1.53/1.71 tff(4229,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4230,plain,
% 1.53/1.71 (((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4231,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4230])).
% 1.53/1.71 tff(4232,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[4231, 4229])).
% 1.53/1.71 tff(4233,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4234,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 1.53/1.71 tff(4235,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4234, 245, 355, 4188, 838, 10, 2653])).
% 1.53/1.71 tff(4236,plain,((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4237,plain,
% 1.53/1.71 (~b(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4236, 4228, 10, 838, 355])).
% 1.53/1.71 tff(4238,plain,
% 1.53/1.71 (r(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[369, 4237, 358])).
% 1.53/1.71 tff(4239,plain,
% 1.53/1.71 (~r(elem!1, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4206, 4238, 572])).
% 1.53/1.71 tff(4240,plain,
% 1.53/1.71 (b(elem!1, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[281, 4239, 3599])).
% 1.53/1.71 tff(4241,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4214, 245, 4105, 4186, 4240, 355])).
% 1.53/1.71 tff(4242,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4243,plain,
% 1.53/1.71 (elem!1 = s(z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4242, 4185, 4105, 4104, 572, 358, 4166, 4160, 4164])).
% 1.53/1.71 tff(4244,plain,
% 1.53/1.71 (s(elem!1) = s(s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4243])).
% 1.53/1.71 tff(4245,plain,
% 1.53/1.71 (s(s(elem!1)) = s(s(s(z)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4244])).
% 1.53/1.71 tff(4246,plain,
% 1.53/1.71 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4245])).
% 1.53/1.71 tff(4247,plain,
% 1.53/1.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4246])).
% 1.53/1.71 tff(4248,plain,
% 1.53/1.71 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4247])).
% 1.53/1.71 tff(4249,plain,
% 1.53/1.71 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.53/1.71 inference(symmetry,[status(thm)],[4248])).
% 1.53/1.71 tff(4250,plain,
% 1.53/1.71 (r(s(s(s(s(z)))), z)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4174, 4249])).
% 1.53/1.71 tff(4251,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4247])).
% 1.53/1.71 tff(4252,plain,
% 1.53/1.71 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4251])).
% 1.53/1.71 tff(4253,plain,
% 1.53/1.71 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4243])).
% 1.53/1.71 tff(4254,plain,
% 1.53/1.71 (b(s(s(s(elem!1))), s(z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1427, 4253])).
% 1.53/1.71 tff(4255,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4254, 4252])).
% 1.53/1.71 tff(4256,plain,
% 1.53/1.71 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4246])).
% 1.53/1.71 tff(4257,plain,
% 1.53/1.71 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4256])).
% 1.53/1.71 tff(4258,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2138])).
% 1.53/1.71 tff(4259,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.71 inference(symmetry,[status(thm)],[4258])).
% 1.53/1.71 tff(4260,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2653, 4259])).
% 1.53/1.71 tff(4261,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8, 4260])).
% 1.53/1.71 tff(4262,plain,((~(elem!1 = s(z))) | b(s(s(s(s(elem!1)))), elem!1) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4263,plain,
% 1.53/1.71 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4262, 4243, 8])).
% 1.53/1.71 tff(4264,plain,
% 1.53/1.71 (r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[217, 4263])).
% 1.53/1.71 tff(4265,plain,
% 1.53/1.71 (r(s(s(s(s(s(z))))), s(z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4264, 4257])).
% 1.53/1.71 tff(4266,plain,
% 1.53/1.71 (~r(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4226, 4264, 4164])).
% 1.53/1.71 tff(4267,plain,
% 1.53/1.71 (b(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1421, 4266])).
% 1.53/1.71 tff(4268,plain,
% 1.53/1.71 (~b(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4196, 4267, 4105, 4160, 4185])).
% 1.53/1.71 tff(4269,plain,
% 1.53/1.71 (r(s(elem!1), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[369, 4268, 358])).
% 1.53/1.71 tff(4270,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4256])).
% 1.53/1.71 tff(4271,plain,
% 1.53/1.71 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4104, 4270])).
% 1.53/1.71 tff(4272,plain,
% 1.53/1.71 (s(s(z)) = s(elem!1)),
% 1.53/1.71 inference(symmetry,[status(thm)],[4244])).
% 1.53/1.71 tff(4273,plain,
% 1.53/1.71 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4272])).
% 1.53/1.71 tff(4274,plain,
% 1.53/1.71 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4273])).
% 1.53/1.71 tff(4275,plain,
% 1.53/1.71 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4256])).
% 1.53/1.71 tff(4276,plain,
% 1.53/1.71 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[556, 4275])).
% 1.53/1.71 tff(4277,plain,
% 1.53/1.71 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4276, 4274])).
% 1.53/1.71 tff(4278,plain,
% 1.53/1.71 (s(s(z)) = s(elem!1)),
% 1.53/1.71 inference(symmetry,[status(thm)],[2139])).
% 1.53/1.71 tff(4279,plain,
% 1.53/1.71 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4278])).
% 1.53/1.71 tff(4280,plain,
% 1.53/1.71 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4279])).
% 1.53/1.71 tff(4281,plain,
% 1.53/1.71 (r(s(s(z)), s(z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[998, 4280])).
% 1.53/1.71 tff(4282,plain,
% 1.53/1.71 ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(z)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[3454, 141, 2203])).
% 1.53/1.71 tff(4283,plain,
% 1.53/1.71 (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4282, 4281])).
% 1.53/1.71 tff(4284,plain,
% 1.53/1.71 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2143])).
% 1.53/1.71 tff(4285,plain,
% 1.53/1.71 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4284])).
% 1.53/1.71 tff(4286,assumption,(s(s(z)) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.53/1.71 tff(4287,plain,
% 1.53/1.71 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4286])).
% 1.53/1.71 tff(4288,plain,
% 1.53/1.71 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(z)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4287])).
% 1.53/1.71 tff(4289,plain,
% 1.53/1.71 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4288])).
% 1.53/1.71 tff(4290,plain,
% 1.53/1.71 (s(z) = s(s(s(s(s(s(z))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[591, 4289, 320, 4285])).
% 1.53/1.71 tff(4291,plain,
% 1.53/1.71 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4290])).
% 1.53/1.71 tff(4292,plain,
% 1.53/1.71 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4291])).
% 1.53/1.71 tff(4293,plain,
% 1.53/1.71 (s(s(s(s(s(z))))) = z),
% 1.53/1.71 inference(transitivity,[status(thm)],[2278, 4292, 52])).
% 1.53/1.71 tff(4294,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[734, 4293])).
% 1.53/1.71 tff(4295,plain,((~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4296,plain,
% 1.53/1.71 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4295, 2138])).
% 1.53/1.71 tff(4297,plain,
% 1.53/1.71 (b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[3459, 32, 4296, 4283])).
% 1.53/1.71 tff(4298,plain,
% 1.53/1.71 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4278])).
% 1.53/1.71 tff(4299,plain,
% 1.53/1.71 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.71 inference(symmetry,[status(thm)],[4298])).
% 1.53/1.71 tff(4300,assumption,(b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.53/1.71 tff(4301,plain,
% 1.53/1.71 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 1.53/1.71 tff(4302,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.71 tff(4303,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4304,plain,
% 1.53/1.71 (((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(4305,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[4304])).
% 1.53/1.71 tff(4306,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[4305, 4303])).
% 1.53/1.71 tff(4307,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(4308,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[4307, 4306])).
% 1.53/1.71 tff(4309,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4308, 245, 4302, 4301, 4297, 2210])).
% 1.53/1.71 tff(4310,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(4311,plain,
% 1.53/1.71 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4310, 4277, 4243, 4271, 332, 4269, 4265])).
% 1.53/1.72 tff(4312,plain,
% 1.53/1.72 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1820, 4311])).
% 1.53/1.72 tff(4313,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4314,plain,
% 1.53/1.72 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4315,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4314])).
% 1.53/1.72 tff(4316,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[4315, 4313])).
% 1.53/1.72 tff(4317,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(4318,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4317, 4316])).
% 1.53/1.72 tff(4319,plain,
% 1.53/1.72 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4318, 245, 4185, 4267, 4312, 4255])).
% 1.53/1.72 tff(4320,plain,
% 1.53/1.72 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2156, 4243, 1])).
% 1.53/1.72 tff(4321,plain,
% 1.53/1.72 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2163, 4320])).
% 1.53/1.72 tff(4322,plain,
% 1.53/1.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4323,plain,
% 1.53/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(4324,plain,
% 1.53/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4323, 4322])).
% 1.53/1.72 tff(4325,plain,
% 1.53/1.72 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4324, 32, 4321, 4319])).
% 1.53/1.72 tff(4326,plain,
% 1.53/1.72 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4247])).
% 1.53/1.72 tff(4327,plain,
% 1.53/1.72 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[4326])).
% 1.53/1.72 tff(4328,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4243])).
% 1.53/1.72 tff(4329,plain,
% 1.53/1.72 (b(s(z), s(s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4150, 4328])).
% 1.53/1.72 tff(4330,plain,
% 1.53/1.72 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4329, 4327])).
% 1.53/1.72 tff(4331,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4332,plain,
% 1.53/1.72 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4333,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4332])).
% 1.53/1.72 tff(4334,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[4333, 4331])).
% 1.53/1.72 tff(4335,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(4336,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4335, 4334])).
% 1.53/1.72 tff(4337,plain,
% 1.53/1.72 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4336, 245, 4267, 4312, 4255, 4330])).
% 1.53/1.72 tff(4338,plain,
% 1.53/1.72 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2220, 32, 1554, 4337])).
% 1.53/1.72 tff(4339,plain,
% 1.53/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4340,plain,
% 1.53/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(4341,plain,
% 1.53/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4340, 4339])).
% 1.53/1.72 tff(4342,plain,
% 1.53/1.72 (~r(s(s(s(s(z)))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4341, 141, 4338, 4325])).
% 1.53/1.72 tff(4343,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4342, 4250])).
% 1.53/1.72 tff(4344,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(z)) | (~b(z, elem!1)) | b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (elem!1 = z) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(4345,plain,
% 1.53/1.72 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4344, 371, 1427, 358, 4105, 8, 1, 572, 3641, 130, 556, 2338])).
% 1.53/1.72 tff(4346,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1239, 4345, 1304])).
% 1.53/1.72 tff(4347,plain,
% 1.53/1.72 (~r(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2393, 141, 1368, 407])).
% 1.53/1.72 tff(4348,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1724, 4347, 1717])).
% 1.53/1.72 tff(4349,plain,
% 1.53/1.72 (~b(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4156, 245, 4105, 1427, 4348])).
% 1.53/1.72 tff(4350,plain,
% 1.53/1.72 (r(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[197, 4349])).
% 1.53/1.72 tff(4351,plain,
% 1.53/1.72 (~r(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[3360, 4350, 407])).
% 1.53/1.72 tff(4352,plain,
% 1.53/1.72 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1992, 4351])).
% 1.53/1.72 tff(4353,plain,
% 1.53/1.72 (~b(z, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2365, 245, 4352, 556, 10])).
% 1.53/1.72 tff(4354,plain,
% 1.53/1.72 (r(z, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[644, 4353])).
% 1.53/1.72 tff(4355,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2416, 141, 371, 4354, 4350])).
% 1.53/1.72 tff(4356,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(4357,plain,
% 1.53/1.72 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4356, 4346, 556, 4104, 4105, 1427, 1673, 371])).
% 1.53/1.72 tff(4358,plain,
% 1.53/1.72 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1432, 4357, 399])).
% 1.53/1.72 tff(4359,plain,
% 1.53/1.72 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4360,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4359])).
% 1.53/1.72 tff(4361,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[4360, 2380])).
% 1.53/1.72 tff(4362,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(4363,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4362, 4361])).
% 1.53/1.72 tff(4364,plain,
% 1.53/1.72 (~b(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4363, 245, 4358, 556, 4104])).
% 1.53/1.72 tff(4365,plain,
% 1.53/1.72 (r(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2777, 4364, 2563])).
% 1.53/1.72 tff(4366,plain,
% 1.53/1.72 (~r(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2772, 4365, 556, 2338, 1312, 130, 4104])).
% 1.53/1.72 tff(4367,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1724, 4366, 1673])).
% 1.53/1.72 tff(4368,plain,
% 1.53/1.72 (~b(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4156, 245, 4105, 1427, 4367])).
% 1.53/1.72 tff(4369,plain,
% 1.53/1.72 (r(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[197, 4368])).
% 1.53/1.72 tff(4370,plain,
% 1.53/1.72 (~r(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[3360, 4369, 4346])).
% 1.53/1.72 tff(4371,plain,
% 1.53/1.72 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1992, 4370])).
% 1.53/1.72 tff(4372,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4373,plain,
% 1.53/1.72 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4374,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4373])).
% 1.53/1.72 tff(4375,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[4374, 4372])).
% 1.53/1.72 tff(4376,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(4377,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4376, 4375])).
% 1.53/1.72 tff(4378,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4377, 245, 4105, 4358, 4371, 556, 4104])).
% 1.53/1.72 tff(4379,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (s(elem!1) = s(z)) | b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(4380,plain,
% 1.53/1.72 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4379, 2574, 4102, 2573, 2570, 2568, 348, 8, 1, 1277, 124])).
% 1.53/1.72 tff(4381,plain,
% 1.53/1.72 (b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[353, 4380, 2569])).
% 1.53/1.72 tff(4382,plain,
% 1.53/1.72 (~b(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2798, 4381, 2574, 7, 2562, 2573, 1277])).
% 1.53/1.72 tff(4383,plain,
% 1.53/1.72 (r(elem!1, s(elem!1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2777, 4382, 2563])).
% 1.53/1.72 tff(4384,plain,
% 1.53/1.72 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1295, 4381, 2574, 2600])).
% 1.53/1.72 tff(4385,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1239, 4384, 1304])).
% 1.53/1.72 tff(4386,plain,
% 1.53/1.72 (~r(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2772, 4383, 2574, 2569, 1312, 2570, 2600])).
% 1.53/1.72 tff(4387,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1724, 4386, 1673])).
% 1.53/1.72 tff(4388,plain,
% 1.53/1.72 (~b(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4156, 245, 4102, 2573, 4387])).
% 1.53/1.72 tff(4389,plain,
% 1.53/1.72 (r(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[197, 4388])).
% 1.53/1.72 tff(4390,plain,
% 1.53/1.72 (~r(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[3360, 4389, 4385])).
% 1.53/1.72 tff(4391,plain,
% 1.53/1.72 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1992, 4390])).
% 1.53/1.72 tff(4392,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4393,plain,
% 1.53/1.72 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(4394,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4393])).
% 1.53/1.72 tff(4395,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[4394, 4392])).
% 1.53/1.72 tff(4396,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(4397,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4396, 4395])).
% 1.53/1.72 tff(4398,plain,
% 1.53/1.72 (~b(s(elem!1), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4397, 245, 4391, 2574, 2600])).
% 1.53/1.72 tff(4399,plain,
% 1.53/1.72 (r(s(elem!1), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1039, 4398])).
% 1.53/1.72 tff(4400,plain,
% 1.53/1.72 (~r(elem!1, z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1082, 4399, 4383])).
% 1.53/1.73 tff(4401,plain,
% 1.53/1.73 (b(elem!1, z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[128, 4400, 124])).
% 1.53/1.73 tff(4402,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4403,plain,
% 1.53/1.73 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4404,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4403])).
% 1.53/1.73 tff(4405,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4404, 4402])).
% 1.53/1.73 tff(4406,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4407,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4406, 4405])).
% 1.53/1.73 tff(4408,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4407, 245, 4105, 1287, 1427, 234, 2101])).
% 1.53/1.73 tff(4409,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(z, 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))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(4410,plain,
% 1.53/1.73 (~b(s(s(s(elem!1))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4409, 4387, 4102, 2573, 4381])).
% 1.53/1.73 tff(4411,plain,
% 1.53/1.73 (r(s(s(s(elem!1))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[37, 4410])).
% 1.53/1.73 tff(4412,plain,
% 1.53/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4413,plain,
% 1.53/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4414,plain,
% 1.53/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4413, 4412])).
% 1.53/1.73 tff(4415,plain,
% 1.53/1.73 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4414, 141, 4399, 4411])).
% 1.53/1.73 tff(4416,plain,
% 1.53/1.73 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2091, 32, 4415])).
% 1.53/1.73 tff(4417,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4416, 2888])).
% 1.53/1.73 tff(4418,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4419,plain,
% 1.53/1.73 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4420,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4419])).
% 1.53/1.73 tff(4421,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4420, 4418])).
% 1.53/1.73 tff(4422,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4423,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4422, 4421])).
% 1.53/1.73 tff(4424,plain,
% 1.53/1.73 (~b(s(z), s(elem!1))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4423, 245, 1287, 2939, 2111])).
% 1.53/1.73 tff(4425,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[440, 4424, 1101, 9])).
% 1.53/1.73 tff(4426,plain,((~r(s(z), z)) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(4427,plain,
% 1.53/1.73 (~r(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4426, 4417, 9, 4399, 4381, 4411])).
% 1.53/1.73 tff(4428,plain,
% 1.53/1.73 (b(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[232, 4427])).
% 1.53/1.73 tff(4429,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4430,plain,
% 1.53/1.73 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4431,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4430])).
% 1.53/1.73 tff(4432,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4431, 4429])).
% 1.53/1.73 tff(4433,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4434,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 1.53/1.73 tff(4435,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4434, 245, 4105, 4186, 355, 447])).
% 1.53/1.73 tff(4436,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(4437,plain,
% 1.53/1.73 (~b(s(z), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4436, 4428, 4102, 4401])).
% 1.53/1.73 tff(4438,plain,
% 1.53/1.73 (((~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(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(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(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4439,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4438])).
% 1.53/1.73 tff(4440,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4439, 2765])).
% 1.53/1.73 tff(4441,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4442,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4441, 4440])).
% 1.53/1.73 tff(4443,plain,
% 1.53/1.73 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4442, 245, 4381, 2574, 2600])).
% 1.53/1.73 tff(4444,plain,
% 1.53/1.73 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1320, 4443, 1312])).
% 1.53/1.73 tff(4445,plain,
% 1.53/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(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(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4446,plain,
% 1.53/1.73 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4447,plain,
% 1.53/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4446])).
% 1.53/1.73 tff(4448,plain,
% 1.53/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4447, 4445])).
% 1.53/1.73 tff(4449,plain,
% 1.53/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4450,plain,
% 1.53/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4449, 4448])).
% 1.53/1.73 tff(4451,plain,
% 1.53/1.73 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4450, 141, 4389, 4444])).
% 1.53/1.73 tff(4452,plain,
% 1.53/1.73 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2558, 4451])).
% 1.53/1.73 tff(4453,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4454,plain,
% 1.53/1.73 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4455,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4454])).
% 1.53/1.73 tff(4456,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4455, 4453])).
% 1.53/1.73 tff(4457,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4458,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4457, 4456])).
% 1.53/1.73 tff(4459,plain,
% 1.53/1.73 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4458, 245, 4102, 4401, 4428, 4452])).
% 1.53/1.73 tff(4460,plain,
% 1.53/1.73 ((s(z) = s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2448, 32, 4459])).
% 1.53/1.73 tff(4461,plain,
% 1.53/1.73 (r(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4460, 2438])).
% 1.53/1.73 tff(4462,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4463,plain,
% 1.53/1.73 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(4464,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4463])).
% 1.53/1.73 tff(4465,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4464, 4462])).
% 1.53/1.73 tff(4466,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(4467,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[4466, 4465])).
% 1.53/1.73 tff(4468,plain,
% 1.53/1.73 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4467, 245, 4102, 4401, 4452])).
% 1.53/1.73 tff(4469,plain,
% 1.53/1.73 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1432, 4468, 2568])).
% 1.53/1.73 tff(4470,plain,
% 1.53/1.73 (~r(s(z), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2458, 141, 4469, 4461])).
% 1.53/1.73 tff(4471,plain,
% 1.53/1.73 (s(z) = elem!1),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[389, 4470, 4437])).
% 1.53/1.73 tff(4472,plain,
% 1.53/1.73 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4471])).
% 1.53/1.73 tff(4473,plain,
% 1.53/1.73 (s(s(z)) = s(elem!1)),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4471])).
% 1.53/1.73 tff(4474,plain,
% 1.53/1.73 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4473])).
% 1.53/1.73 tff(4475,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[4474])).
% 1.53/1.73 tff(4476,plain,
% 1.53/1.73 (s(s(s(z))) = s(s(elem!1))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4473])).
% 1.53/1.73 tff(4477,plain,
% 1.53/1.73 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4476])).
% 1.53/1.73 tff(4478,plain,
% 1.53/1.73 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4477])).
% 1.53/1.73 tff(4479,plain,
% 1.53/1.73 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[4478])).
% 1.53/1.73 tff(4480,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[4479])).
% 1.53/1.73 tff(4481,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[4480, 4475])).
% 1.53/1.73 tff(4482,plain,
% 1.53/1.73 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2574, 4481])).
% 1.53/1.74 tff(4483,plain,
% 1.53/1.74 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4471])).
% 1.53/1.74 tff(4484,plain,
% 1.53/1.74 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.53/1.74 inference(symmetry,[status(thm)],[4483])).
% 1.53/1.74 tff(4485,plain,
% 1.53/1.74 (r(s(elem!1), s(z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1277, 4484])).
% 1.53/1.74 tff(4486,plain,
% 1.53/1.74 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4478])).
% 1.53/1.74 tff(4487,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.74 inference(symmetry,[status(thm)],[4486])).
% 1.53/1.74 tff(4488,plain,
% 1.53/1.74 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2600, 4487])).
% 1.53/1.74 tff(4489,plain,
% 1.53/1.74 (~b(elem!1, s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4214, 245, 4102, 4401, 4428])).
% 1.53/1.74 tff(4490,plain,
% 1.53/1.74 (~r(elem!1, s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2481, 141, 4469, 4461])).
% 1.53/1.74 tff(4491,plain,
% 1.53/1.74 (elem!1 = s(z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[281, 4490, 4489])).
% 1.53/1.74 tff(4492,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4471])).
% 1.53/1.74 tff(4493,plain,
% 1.53/1.74 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.53/1.74 inference(symmetry,[status(thm)],[4492])).
% 1.53/1.74 tff(4494,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.53/1.74 tff(4495,assumption,(~r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.53/1.74 tff(4496,plain,
% 1.53/1.74 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[771])).
% 1.53/1.74 tff(4497,plain,
% 1.53/1.74 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(z))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4496, 338])).
% 1.53/1.74 tff(4498,plain,
% 1.53/1.74 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = elem!1)),
% 1.53/1.74 inference(transitivity,[status(thm)],[4497, 339])).
% 1.53/1.74 tff(4499,plain,
% 1.53/1.74 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = elem!1))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4498])).
% 1.53/1.74 tff(4500,plain,
% 1.53/1.74 (~(s(z) = elem!1)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[702, 4499])).
% 1.53/1.74 tff(4501,plain,
% 1.53/1.74 (b(s(z), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[389, 4500, 4494])).
% 1.53/1.74 tff(4502,plain,
% 1.53/1.74 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(z)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4497])).
% 1.53/1.74 tff(4503,plain,
% 1.53/1.74 (~(elem!1 = s(z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[702, 4502])).
% 1.53/1.74 tff(4504,plain,
% 1.53/1.74 (~r(s(elem!1), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4206, 268, 1277])).
% 1.53/1.74 tff(4505,plain,
% 1.53/1.74 (b(s(elem!1), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[369, 4504, 348])).
% 1.53/1.74 tff(4506,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4507,plain,
% 1.53/1.74 (((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4508,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4507])).
% 1.53/1.74 tff(4509,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4508, 4506])).
% 1.53/1.74 tff(4510,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(4511,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4510, 4509])).
% 1.53/1.74 tff(4512,plain,
% 1.53/1.74 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4511, 245, 4105, 4186, 1943])).
% 1.53/1.74 tff(4513,plain,
% 1.53/1.74 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[151, 4512, 2562])).
% 1.53/1.74 tff(4514,plain,
% 1.53/1.74 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1284, 4513, 1277])).
% 1.53/1.74 tff(4515,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[420, 4514, 7])).
% 1.53/1.74 tff(4516,plain,
% 1.53/1.74 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1274, 4513, 1, 564])).
% 1.53/1.74 tff(4517,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4518,plain,
% 1.53/1.74 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4519,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4518])).
% 1.53/1.74 tff(4520,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4519, 4517])).
% 1.53/1.74 tff(4521,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(4522,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4521, 4520])).
% 1.53/1.74 tff(4523,plain,
% 1.53/1.74 (~b(s(s(s(elem!1))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4522, 245, 4105, 4186, 234])).
% 1.53/1.74 tff(4524,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4525,plain,
% 1.53/1.74 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4526,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4525])).
% 1.53/1.74 tff(4527,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4526, 4524])).
% 1.53/1.74 tff(4528,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(4529,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4528, 4527])).
% 1.53/1.74 tff(4530,plain,
% 1.53/1.74 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4529, 245, 4105, 4186, 234, 1943])).
% 1.53/1.74 tff(4531,plain,
% 1.53/1.74 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1257, 4530, 1, 4523])).
% 1.53/1.74 tff(4532,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[151, 4531, 4512, 2562])).
% 1.53/1.74 tff(4533,plain,((~b(s(s(s(s(elem!1)))), z)) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(4534,plain,
% 1.53/1.74 (~b(s(s(s(elem!1))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4533, 1943, 1, 4105, 4186, 2562])).
% 1.53/1.74 tff(4535,plain,
% 1.53/1.74 (r(s(s(s(elem!1))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[37, 4534])).
% 1.53/1.74 tff(4536,plain,
% 1.53/1.74 (~r(s(s(s(elem!1))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2177, 4535, 220])).
% 1.53/1.74 tff(4537,plain,
% 1.53/1.74 (b(s(s(s(elem!1))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[265, 4536])).
% 1.53/1.74 tff(4538,plain,
% 1.53/1.74 (~r(s(z), s(s(s(elem!1))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2109, 4535, 220])).
% 1.53/1.74 tff(4539,plain,
% 1.53/1.74 (b(s(z), s(s(s(elem!1))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1133, 4538])).
% 1.53/1.74 tff(4540,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4541,plain,
% 1.53/1.74 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4542,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4541])).
% 1.53/1.74 tff(4543,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4542, 4540])).
% 1.53/1.74 tff(4544,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(4545,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4544, 4543])).
% 1.53/1.74 tff(4546,plain,
% 1.53/1.74 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4545, 245, 4188, 4539, 4537])).
% 1.53/1.74 tff(4547,plain,
% 1.53/1.74 (r(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[353, 4546, 11])).
% 1.53/1.74 tff(4548,plain,
% 1.53/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4549,plain,
% 1.53/1.74 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4550,plain,
% 1.53/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4549])).
% 1.53/1.74 tff(4551,plain,
% 1.53/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4550, 4548])).
% 1.53/1.74 tff(4552,plain,
% 1.53/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(4553,plain,
% 1.53/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4552, 4551])).
% 1.53/1.74 tff(4554,plain,
% 1.53/1.74 (~r(s(s(s(elem!1))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4553, 141, 371, 1342])).
% 1.53/1.74 tff(4555,plain,
% 1.53/1.74 (b(s(s(s(elem!1))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[37, 4554])).
% 1.53/1.74 tff(4556,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4557,plain,
% 1.53/1.74 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4558,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4557])).
% 1.53/1.74 tff(4559,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4558, 4556])).
% 1.53/1.74 tff(4560,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(4561,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4560, 4559])).
% 1.53/1.74 tff(4562,plain,
% 1.53/1.74 ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4561, 245])).
% 1.53/1.74 tff(4563,plain,
% 1.53/1.74 (~b(s(s(s(elem!1))), elem!1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4562, 2418, 4186, 4555])).
% 1.53/1.74 tff(4564,plain,
% 1.53/1.74 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1257, 4563, 1, 130])).
% 1.53/1.74 tff(4565,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4566,plain,
% 1.53/1.74 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(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(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4567,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[4566])).
% 1.53/1.74 tff(4568,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[4567, 4565])).
% 1.53/1.74 tff(4569,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(4570,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[4569, 4568])).
% 1.53/1.74 tff(4571,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4570, 245, 2418, 4555, 4564, 1943])).
% 1.53/1.74 tff(4572,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(4573,plain,
% 1.53/1.74 (~r(z, s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4572, 4547, 1, 4186, 1943, 4513])).
% 1.53/1.74 tff(4574,plain,
% 1.53/1.74 (b(z, s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[644, 4573])).
% 1.53/1.74 tff(4575,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4576,plain,
% 1.53/1.74 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(4577,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4576])).
% 1.53/1.75 tff(4578,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4577, 4575])).
% 1.53/1.75 tff(4579,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4580,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 1.53/1.75 tff(4581,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4580, 245, 4574, 4516, 1943, 4515])).
% 1.53/1.75 tff(4582,plain,((~b(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(elem!1, z)) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(elem!1), s(z))) | (~b(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(4583,plain,
% 1.53/1.75 (~b(s(s(s(s(elem!1)))), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4582, 4186, 1, 564, 11, 2562, 4188, 4105, 220])).
% 1.53/1.75 tff(4584,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2558, 4583])).
% 1.53/1.75 tff(4585,plain,
% 1.53/1.75 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[3376, 141, 220, 4584])).
% 1.53/1.75 tff(4586,plain,
% 1.53/1.75 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2448, 32, 4585])).
% 1.53/1.75 tff(4587,plain,
% 1.53/1.75 (b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4586, 2438])).
% 1.53/1.75 tff(4588,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4589,plain,
% 1.53/1.75 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4590,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4589])).
% 1.53/1.75 tff(4591,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4590, 4588])).
% 1.53/1.75 tff(4592,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4593,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4592, 4591])).
% 1.53/1.75 tff(4594,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4593, 245, 4105, 4186, 447, 4187])).
% 1.53/1.75 tff(4595,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(4596,plain,
% 1.53/1.75 (~b(z, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4595, 4186, 447, 4105])).
% 1.53/1.75 tff(4597,plain,
% 1.53/1.75 (r(z, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1421, 4596])).
% 1.53/1.75 tff(4598,plain,
% 1.53/1.75 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4226, 4584, 4597])).
% 1.53/1.75 tff(4599,plain,
% 1.53/1.75 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[217, 4598])).
% 1.53/1.75 tff(4600,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4601,plain,
% 1.53/1.75 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4602,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4601])).
% 1.53/1.75 tff(4603,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4602, 4600])).
% 1.53/1.75 tff(4604,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4605,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4604, 4603])).
% 1.53/1.75 tff(4606,plain,
% 1.53/1.75 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4605, 245, 655, 4188, 4599])).
% 1.53/1.75 tff(4607,plain,
% 1.53/1.75 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1274, 4606, 1, 564])).
% 1.53/1.75 tff(4608,plain,
% 1.53/1.75 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[151, 4607, 2562])).
% 1.53/1.75 tff(4609,plain,
% 1.53/1.75 (r(elem!1, s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[422])).
% 1.53/1.75 tff(4610,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[268, 4609])).
% 1.53/1.75 tff(4611,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[212, 4610])).
% 1.53/1.75 tff(4612,plain,((~r(elem!1, s(z))) | r(s(s(s(s(elem!1)))), s(z)) | (~(elem!1 = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(4613,plain,
% 1.53/1.75 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4612, 4598, 268])).
% 1.53/1.75 tff(4614,plain,
% 1.53/1.75 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1263, 4606, 1])).
% 1.53/1.75 tff(4615,plain,
% 1.53/1.75 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2837, 4614, 1277])).
% 1.53/1.75 tff(4616,plain,
% 1.53/1.75 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1432, 4615, 4613])).
% 1.53/1.75 tff(4617,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4618,plain,
% 1.53/1.75 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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)))))) | (~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)))))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4619,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4618])).
% 1.53/1.75 tff(4620,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4619, 4617])).
% 1.53/1.75 tff(4621,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4622,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 1.53/1.75 tff(4623,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4622, 245, 4616, 447, 4608, 4587])).
% 1.53/1.75 tff(4624,plain,((~b(elem!1, z)) | (~b(s(z), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(4625,plain,
% 1.53/1.75 (~b(elem!1, z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4624, 220, 2562, 1, 564, 655, 4188, 447, 268, 11, 4105])).
% 1.53/1.75 tff(4626,plain,
% 1.53/1.75 (r(elem!1, z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[128, 4625, 3641])).
% 1.53/1.75 tff(4627,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2099, 141, 4626, 268, 220])).
% 1.53/1.75 tff(4628,plain,((~r(s(z), z)) | (~r(elem!1, s(z))) | (elem!1 = z) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(4629,plain,
% 1.53/1.75 (~r(s(z), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4628, 655, 3641, 2562, 1, 564, 268, 4188, 447, 11, 4105])).
% 1.53/1.75 tff(4630,plain,
% 1.53/1.75 (b(s(z), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[232, 4629])).
% 1.53/1.75 tff(4631,plain,
% 1.53/1.75 (~b(elem!1, z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4436, 4630, 4105, 447])).
% 1.53/1.75 tff(4632,plain,
% 1.53/1.75 (r(elem!1, z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[128, 4631, 3641])).
% 1.53/1.75 tff(4633,plain,
% 1.53/1.75 (((~![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))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4634,plain,
% 1.53/1.75 (((~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))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4635,plain,
% 1.53/1.75 (((~![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)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4634])).
% 1.53/1.75 tff(4636,plain,
% 1.53/1.75 (((~![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))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4635, 4633])).
% 1.53/1.75 tff(4637,plain,
% 1.53/1.75 ((~![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)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4638,plain,
% 1.53/1.75 ((~![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)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4637, 4636])).
% 1.53/1.75 tff(4639,plain,
% 1.53/1.75 ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4638, 141])).
% 1.53/1.75 tff(4640,plain,
% 1.53/1.75 (~r(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4639, 4632, 1367])).
% 1.53/1.75 tff(4641,plain,
% 1.53/1.75 (b(z, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[644, 4640])).
% 1.53/1.75 tff(4642,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4643,plain,
% 1.53/1.75 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4644,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4643])).
% 1.53/1.75 tff(4645,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4644, 4642])).
% 1.53/1.75 tff(4646,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4647,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4646, 4645])).
% 1.53/1.75 tff(4648,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4647, 245, 4630, 655, 4188, 4641])).
% 1.53/1.75 tff(4649,plain,((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (elem!1 = z) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(4650,plain,
% 1.53/1.75 (~b(s(z), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4649, 4505, 1367, 124, 4105, 447, 2562, 1, 564, 268, 11])).
% 1.53/1.75 tff(4651,plain,
% 1.53/1.75 (r(s(z), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[440, 4650, 9])).
% 1.53/1.75 tff(4652,plain,
% 1.53/1.75 (((~![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(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(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4653,plain,
% 1.53/1.75 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4654,plain,
% 1.53/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4653])).
% 1.53/1.75 tff(4655,plain,
% 1.53/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4654, 4652])).
% 1.53/1.75 tff(4656,plain,
% 1.53/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4657,plain,
% 1.53/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4656, 4655])).
% 1.53/1.75 tff(4658,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4657, 141, 1367, 268, 4651])).
% 1.53/1.75 tff(4659,plain,((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(4660,plain,
% 1.53/1.75 (~r(elem!1, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4659, 1367, 9, 4105, 447, 2562, 1, 564, 11])).
% 1.53/1.75 tff(4661,plain,
% 1.53/1.75 (b(elem!1, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[281, 4660, 3599])).
% 1.53/1.75 tff(4662,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4663,plain,
% 1.53/1.75 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4664,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[4663])).
% 1.53/1.75 tff(4665,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[4664, 4662])).
% 1.53/1.75 tff(4666,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(4667,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[4666, 4665])).
% 1.53/1.75 tff(4668,plain,
% 1.53/1.75 (~b(z, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[4667, 245, 4105, 301, 447])).
% 1.53/1.75 tff(4669,plain,
% 1.53/1.75 (r(z, s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1421, 4668])).
% 1.53/1.75 tff(4670,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4671,plain,
% 1.53/1.75 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(4672,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4671])).
% 1.53/1.76 tff(4673,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4672, 4670])).
% 1.53/1.76 tff(4674,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4675,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 1.53/1.76 tff(4676,plain,
% 1.53/1.76 (~b(s(s(s(s(elem!1)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4675, 245, 4105, 301, 447, 2824])).
% 1.53/1.76 tff(4677,plain,
% 1.53/1.76 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2558, 4676])).
% 1.53/1.76 tff(4678,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4679,plain,
% 1.53/1.76 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4680,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4679])).
% 1.53/1.76 tff(4681,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4680, 4678])).
% 1.53/1.76 tff(4682,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4683,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[4682, 4681])).
% 1.53/1.76 tff(4684,plain,
% 1.53/1.76 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4683, 245, 301, 447, 2824])).
% 1.53/1.76 tff(4685,plain,
% 1.53/1.76 (r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[217, 4684])).
% 1.53/1.76 tff(4686,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4226, 4685, 4677, 4669])).
% 1.53/1.76 tff(4687,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(4688,plain,
% 1.53/1.76 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4687, 4661, 447, 4105])).
% 1.53/1.76 tff(4689,plain,
% 1.53/1.76 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[151, 4688, 2562])).
% 1.53/1.76 tff(4690,plain,
% 1.53/1.76 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1284, 4689, 1277])).
% 1.53/1.76 tff(4691,plain,
% 1.53/1.76 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[420, 4690, 7])).
% 1.53/1.76 tff(4692,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4693,plain,
% 1.53/1.76 (((~b(s(z), elem!1)) | (~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), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4694,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(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(X0, 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(s(z), elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4693])).
% 1.53/1.76 tff(4695,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(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(X0, 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(s(z), elem!1)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4694, 4692])).
% 1.53/1.76 tff(4696,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4697,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[4696, 4695])).
% 1.53/1.76 tff(4698,plain,
% 1.53/1.76 (~b(s(z), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4697, 245, 4105, 301, 447])).
% 1.53/1.76 tff(4699,plain,
% 1.53/1.76 (r(s(z), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[232, 4698])).
% 1.53/1.76 tff(4700,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4701,plain,
% 1.53/1.76 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4702,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4701])).
% 1.53/1.76 tff(4703,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4702, 4700])).
% 1.53/1.76 tff(4704,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4705,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[4704, 4703])).
% 1.53/1.76 tff(4706,plain,
% 1.53/1.76 (~b(s(s(s(elem!1))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4705, 245, 301, 4539, 4537])).
% 1.53/1.76 tff(4707,plain,
% 1.53/1.76 (r(s(s(s(elem!1))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[110, 4706, 96])).
% 1.53/1.76 tff(4708,plain,
% 1.53/1.76 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1257, 4706, 1, 4513])).
% 1.53/1.76 tff(4709,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1297, 4708, 4707, 11, 4513, 564, 1])).
% 1.53/1.76 tff(4710,plain,((~b(s(s(s(s(elem!1)))), z)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(4711,plain,
% 1.53/1.76 (~b(s(s(s(s(elem!1)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4710, 4186, 564, 1, 2562, 301, 4105, 11, 4699])).
% 1.53/1.76 tff(4712,plain,
% 1.53/1.76 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2558, 4711])).
% 1.53/1.76 tff(4713,plain,
% 1.53/1.76 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3376, 141, 4699, 4712])).
% 1.53/1.76 tff(4714,plain,
% 1.53/1.76 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2448, 32, 4713])).
% 1.53/1.76 tff(4715,plain,
% 1.53/1.76 (b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4714, 2438])).
% 1.53/1.76 tff(4716,plain,
% 1.53/1.76 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4226, 4712, 4669])).
% 1.53/1.76 tff(4717,plain,
% 1.53/1.76 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[217, 4716])).
% 1.53/1.76 tff(4718,plain,
% 1.53/1.76 (((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4719,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4718])).
% 1.53/1.76 tff(4720,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4719, 4678])).
% 1.53/1.76 tff(4721,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4722,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[4721, 4720])).
% 1.53/1.76 tff(4723,plain,
% 1.53/1.76 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4722, 245, 301, 447, 4717])).
% 1.53/1.76 tff(4724,plain,
% 1.53/1.76 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[151, 4723, 2562])).
% 1.53/1.76 tff(4725,plain,
% 1.53/1.76 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1284, 4724, 1277])).
% 1.53/1.76 tff(4726,plain,
% 1.53/1.76 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[420, 4725, 7])).
% 1.53/1.76 tff(4727,plain,
% 1.53/1.76 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1274, 4724, 1, 564])).
% 1.53/1.76 tff(4728,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), 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(X0, 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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4729,plain,
% 1.53/1.76 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4730,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4729])).
% 1.53/1.76 tff(4731,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4730, 4728])).
% 1.53/1.76 tff(4732,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4733,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[4732, 4731])).
% 1.53/1.76 tff(4734,plain,
% 1.53/1.76 (~b(s(elem!1), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4733, 245, 4727, 4726, 4715])).
% 1.53/1.76 tff(4735,plain,
% 1.53/1.76 (r(s(elem!1), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[369, 4734, 348])).
% 1.53/1.76 tff(4736,plain,
% 1.53/1.76 (((~![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))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4737,plain,
% 1.53/1.76 (((~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))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4738,plain,
% 1.53/1.76 (((~![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)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4737])).
% 1.53/1.76 tff(4739,plain,
% 1.53/1.76 (((~![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))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4738, 4736])).
% 1.53/1.76 tff(4740,plain,
% 1.53/1.76 ((~![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))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4741,plain,
% 1.53/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[4740, 4739])).
% 1.53/1.76 tff(4742,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4741, 141, 1342, 998, 1449])).
% 1.53/1.76 tff(4743,plain,((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(4744,plain,
% 1.53/1.76 (~r(z, s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4743, 4735, 4669])).
% 1.53/1.76 tff(4745,plain,
% 1.53/1.76 (b(z, s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[644, 4744])).
% 1.53/1.76 tff(4746,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4747,plain,
% 1.53/1.76 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(4748,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[4747])).
% 1.53/1.76 tff(4749,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[4748, 4746])).
% 1.53/1.76 tff(4750,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(4751,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4750, 4749])).
% 1.53/1.77 tff(4752,plain,
% 1.53/1.77 ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4751, 245, 4105, 447, 4727, 4717])).
% 1.53/1.77 tff(4753,plain,
% 1.53/1.77 (~b(z, s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4752, 4745])).
% 1.53/1.77 tff(4754,plain,
% 1.53/1.77 (r(z, s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1992, 4753])).
% 1.53/1.77 tff(4755,plain,
% 1.53/1.77 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1239, 305, 1304])).
% 1.53/1.77 tff(4756,plain,
% 1.53/1.77 (~r(z, s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3360, 4755, 310])).
% 1.53/1.77 tff(4757,plain,
% 1.53/1.77 (b(z, s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[197, 4756])).
% 1.53/1.77 tff(4758,plain,
% 1.53/1.77 (~b(s(s(s(elem!1))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4562, 4757, 4186, 2013])).
% 1.53/1.77 tff(4759,plain,
% 1.53/1.77 (r(s(s(s(elem!1))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[37, 4758])).
% 1.53/1.77 tff(4760,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3336, 141, 4759, 310, 4755])).
% 1.53/1.77 tff(4761,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(4762,plain,
% 1.53/1.77 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4761, 4754, 4186, 1, 4724])).
% 1.53/1.77 tff(4763,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4764,plain,
% 1.53/1.77 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4765,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), 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(z), s(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(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4764])).
% 1.53/1.77 tff(4766,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), 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(z), s(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(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[4765, 4763])).
% 1.53/1.77 tff(4767,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(4768,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4767, 4766])).
% 1.53/1.77 tff(4769,plain,
% 1.53/1.77 (~b(s(z), s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4768, 245, 4727, 4762, 4726, 4715])).
% 1.53/1.77 tff(4770,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(elem!1))) | (~b(s(z), 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(X0, 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(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4771,plain,
% 1.53/1.77 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4772,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4771])).
% 1.53/1.77 tff(4773,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[4772, 4770])).
% 1.53/1.77 tff(4774,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(elem!1))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(4775,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4774, 4773])).
% 1.53/1.77 tff(4776,plain,
% 1.53/1.77 (~b(s(z), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4775, 245, 4727, 4726, 4715])).
% 1.53/1.77 tff(4777,plain,
% 1.53/1.77 (r(s(z), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[440, 4776, 9])).
% 1.53/1.77 tff(4778,plain,
% 1.53/1.77 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1295, 4762, 4726, 4727])).
% 1.53/1.77 tff(4779,plain,
% 1.53/1.77 (r(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[353, 4778, 11])).
% 1.53/1.77 tff(4780,plain,
% 1.53/1.77 (~r(s(z), s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2411, 141, 4779, 4777])).
% 1.53/1.77 tff(4781,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1133, 4780, 4769])).
% 1.53/1.77 tff(4782,plain,((~b(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(z) = s(elem!1)) | b(s(elem!1), elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(4783,plain,
% 1.53/1.77 (~b(elem!1, z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4782, 4661, 1, 4105, 447, 9, 564, 2562, 11])).
% 1.53/1.77 tff(4784,plain,
% 1.53/1.77 (r(elem!1, z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[128, 4783, 124])).
% 1.53/1.77 tff(4785,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[146, 4689, 4784])).
% 1.53/1.77 tff(4786,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2558, 4785])).
% 1.53/1.77 tff(4787,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1274, 4689, 1, 564])).
% 1.53/1.77 tff(4788,plain,
% 1.53/1.77 (~r(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4639, 4784, 1367])).
% 1.53/1.77 tff(4789,plain,
% 1.53/1.77 (b(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[644, 4788])).
% 1.53/1.77 tff(4790,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4580, 245, 4789, 4787, 4786, 4691])).
% 1.53/1.77 tff(4791,plain,((~r(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(4792,plain,
% 1.53/1.77 (~r(elem!1, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4791, 4501, 564, 2562, 1, 4105, 9, 11, 4503])).
% 1.53/1.77 tff(4793,plain,
% 1.53/1.77 (b(elem!1, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2777, 4792, 2563])).
% 1.53/1.77 tff(4794,plain,
% 1.53/1.77 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4687, 301, 447, 4105])).
% 1.53/1.77 tff(4795,plain,
% 1.53/1.77 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[151, 4794, 2562])).
% 1.53/1.77 tff(4796,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1284, 4795, 1277])).
% 1.53/1.77 tff(4797,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[420, 4796, 7])).
% 1.53/1.77 tff(4798,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1274, 4795, 1, 564])).
% 1.53/1.77 tff(4799,plain,
% 1.53/1.77 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2385, 245, 1103, 4798, 4797])).
% 1.53/1.77 tff(4800,plain,
% 1.53/1.77 (~b(elem!1, z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4782, 301, 1, 4105, 447, 9, 564, 2562, 11])).
% 1.53/1.77 tff(4801,plain,
% 1.53/1.77 (r(elem!1, z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[128, 4800, 124])).
% 1.53/1.77 tff(4802,assumption,(~b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.77 tff(4803,plain,
% 1.53/1.77 (b(z, elem!1) <=> b(z, s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[422])).
% 1.53/1.77 tff(4804,plain,
% 1.53/1.77 (b(z, s(s(s(s(elem!1))))) <=> b(z, elem!1)),
% 1.53/1.77 inference(symmetry,[status(thm)],[4803])).
% 1.53/1.77 tff(4805,plain,
% 1.53/1.77 ((~b(z, s(s(s(s(elem!1)))))) <=> (~b(z, elem!1))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4804])).
% 1.53/1.77 tff(4806,plain,
% 1.53/1.77 (~b(z, elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3523, 4805])).
% 1.53/1.77 tff(4807,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4105, 4806])).
% 1.53/1.77 tff(4808,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | b(z, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(4809,plain,
% 1.53/1.77 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4808, 3523, 4105])).
% 1.53/1.77 tff(4810,plain,
% 1.53/1.77 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1432, 4809, 4802])).
% 1.53/1.77 tff(4811,plain,
% 1.53/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(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, z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4812,plain,
% 1.53/1.77 (((~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4813,plain,
% 1.53/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4812])).
% 1.53/1.77 tff(4814,plain,
% 1.53/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[4813, 4811])).
% 1.53/1.77 tff(4815,plain,
% 1.53/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, z)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(4816,plain,
% 1.53/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 1.53/1.77 tff(4817,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4816, 141, 131, 4810, 3526])).
% 1.53/1.77 tff(4818,plain,(b(z, s(s(s(s(elem!1))))) | (~r(elem!1, z)) | b(elem!1, s(s(s(s(elem!1))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(4819,plain,
% 1.53/1.77 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4818, 4801, 4799, 4105])).
% 1.53/1.77 tff(4820,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[146, 4795, 4801])).
% 1.53/1.77 tff(4821,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2558, 4820])).
% 1.53/1.77 tff(4822,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4823,plain,
% 1.53/1.77 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4824,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4823])).
% 1.53/1.77 tff(4825,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[4824, 4822])).
% 1.53/1.77 tff(4826,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(4827,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4826, 4825])).
% 1.53/1.77 tff(4828,plain,
% 1.53/1.77 ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4827, 245, 4105, 4798, 4821])).
% 1.53/1.77 tff(4829,plain,
% 1.53/1.77 (~b(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4828, 4819])).
% 1.53/1.77 tff(4830,plain,
% 1.53/1.77 (r(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[644, 4829])).
% 1.53/1.77 tff(4831,plain,
% 1.53/1.77 (~r(s(elem!1), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4743, 4830, 4669])).
% 1.53/1.77 tff(4832,plain,
% 1.53/1.77 (b(s(elem!1), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[369, 4831, 348])).
% 1.53/1.77 tff(4833,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4834,plain,
% 1.53/1.77 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4835,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4834])).
% 1.53/1.77 tff(4836,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[4835, 4833])).
% 1.53/1.77 tff(4837,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(4838,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4837, 4836])).
% 1.53/1.77 tff(4839,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4838, 245, 301, 1103, 4832, 447])).
% 1.53/1.77 tff(4840,plain,((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(4841,plain,
% 1.53/1.77 (~b(elem!1, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4840, 4793, 4501, 4105, 1, 564, 2562, 9, 11])).
% 1.53/1.77 tff(4842,plain,
% 1.53/1.77 (r(elem!1, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[281, 4841, 4503])).
% 1.53/1.77 tff(4843,plain,
% 1.53/1.77 (~r(s(elem!1), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4206, 4842, 1277])).
% 1.53/1.77 tff(4844,plain,
% 1.53/1.77 (b(s(elem!1), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[369, 4843, 348])).
% 1.53/1.77 tff(4845,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4846,plain,
% 1.53/1.77 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4847,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4846])).
% 1.53/1.77 tff(4848,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[4847, 4845])).
% 1.53/1.77 tff(4849,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(4850,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4849, 4848])).
% 1.53/1.77 tff(4851,plain,
% 1.53/1.77 (~b(s(z), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4850, 245, 4793, 4844, 4501])).
% 1.53/1.77 tff(4852,plain,
% 1.53/1.77 (r(s(z), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[440, 4851, 9])).
% 1.53/1.77 tff(4853,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4854,plain,
% 1.53/1.77 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(4855,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[4854])).
% 1.53/1.77 tff(4856,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[4855, 4853])).
% 1.53/1.77 tff(4857,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(4858,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[4857, 4856])).
% 1.53/1.77 tff(4859,plain,
% 1.53/1.77 (~b(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4858, 245, 4105, 4793, 4844, 4501])).
% 1.53/1.77 tff(4860,plain,
% 1.53/1.77 (r(z, s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[644, 4859])).
% 1.53/1.77 tff(4861,plain,
% 1.53/1.77 (~r(z, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2403, 141, 4860, 4852])).
% 1.53/1.77 tff(4862,plain,
% 1.53/1.77 (b(z, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1421, 4861])).
% 1.53/1.77 tff(4863,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4864,plain,
% 1.53/1.78 (((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4865,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4864])).
% 1.53/1.78 tff(4866,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4865, 4863])).
% 1.53/1.78 tff(4867,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(4868,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4867, 4866])).
% 1.53/1.78 tff(4869,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4868, 245, 4105, 4793, 4844, 4501, 4862])).
% 1.53/1.78 tff(4870,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~b(z, elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(4871,plain,
% 1.53/1.78 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4870, 4105, 9, 1, 564, 2562, 11, 4494])).
% 1.53/1.78 tff(4872,plain,
% 1.53/1.78 (b(s(s(s(s(s(z))))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[787, 4871, 4495])).
% 1.53/1.78 tff(4873,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2898])).
% 1.53/1.78 tff(4874,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.78 inference(symmetry,[status(thm)],[4873])).
% 1.53/1.78 tff(4875,plain,
% 1.53/1.78 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2910])).
% 1.53/1.78 tff(4876,plain,
% 1.53/1.78 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4875])).
% 1.53/1.78 tff(4877,plain,
% 1.53/1.78 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4876, 4874])).
% 1.53/1.78 tff(4878,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.53/1.78 tff(4879,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4878, 4877])).
% 1.53/1.78 tff(4880,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4878, 4876])).
% 1.53/1.78 tff(4881,plain,
% 1.53/1.78 (s(s(elem!1)) = s(s(s(z)))),
% 1.53/1.78 inference(symmetry,[status(thm)],[2909])).
% 1.53/1.78 tff(4882,plain,
% 1.53/1.78 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4881])).
% 1.53/1.78 tff(4883,plain,
% 1.53/1.78 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.53/1.78 inference(symmetry,[status(thm)],[4882])).
% 1.53/1.78 tff(4884,plain,
% 1.53/1.78 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[2898])).
% 1.53/1.78 tff(4885,plain,
% 1.53/1.78 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(s(z))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4884, 686])).
% 1.53/1.78 tff(4886,plain,
% 1.53/1.78 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4885])).
% 1.53/1.78 tff(4887,plain,
% 1.53/1.78 (~(elem!1 = s(s(s(z))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[892, 4886])).
% 1.53/1.78 tff(4888,plain,
% 1.53/1.78 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4881])).
% 1.53/1.78 tff(4889,plain,
% 1.53/1.78 ((~b(elem!1, s(s(elem!1)))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4888])).
% 1.53/1.78 tff(4890,plain,
% 1.53/1.78 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4881])).
% 1.53/1.78 tff(4891,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(symmetry,[status(thm)],[4890])).
% 1.53/1.78 tff(4892,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4875])).
% 1.53/1.78 tff(4893,plain,
% 1.53/1.78 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4875])).
% 1.53/1.78 tff(4894,plain,
% 1.53/1.78 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.78 inference(symmetry,[status(thm)],[4893])).
% 1.53/1.78 tff(4895,plain,
% 1.53/1.78 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4881])).
% 1.53/1.78 tff(4896,plain,
% 1.53/1.78 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4895, 4894])).
% 1.53/1.78 tff(4897,plain,
% 1.53/1.78 ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4896])).
% 1.53/1.78 tff(4898,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4899,plain,
% 1.53/1.78 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4900,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4899])).
% 1.53/1.78 tff(4901,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4900, 4898])).
% 1.53/1.78 tff(4902,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(4903,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 1.53/1.78 tff(4904,plain,
% 1.53/1.78 (~b(z, s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4903, 245, 4105, 4186, 2824])).
% 1.53/1.78 tff(4905,plain,
% 1.53/1.78 (r(z, s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1992, 4904])).
% 1.53/1.78 tff(4906,plain,
% 1.53/1.78 (~b(z, s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4136, 245, 4105, 4186, 1427])).
% 1.53/1.78 tff(4907,plain,
% 1.53/1.78 (r(z, s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[197, 4906])).
% 1.53/1.78 tff(4908,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4909,plain,
% 1.53/1.78 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4910,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4909])).
% 1.53/1.78 tff(4911,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4910, 4908])).
% 1.53/1.78 tff(4912,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(4913,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4912, 4911])).
% 1.53/1.78 tff(4914,plain,
% 1.53/1.78 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4913, 245, 4105, 4186, 1427, 2824])).
% 1.53/1.78 tff(4915,plain,
% 1.53/1.78 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1239, 4914, 1309])).
% 1.53/1.78 tff(4916,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3360, 4915, 4907, 4905])).
% 1.53/1.78 tff(4917,plain,((~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(4918,plain,
% 1.53/1.78 (~b(s(s(s(elem!1))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4917, 4186, 4105, 1304, 2824])).
% 1.53/1.78 tff(4919,plain,
% 1.53/1.78 (r(s(s(s(elem!1))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[110, 4918, 96])).
% 1.53/1.78 tff(4920,plain,
% 1.53/1.78 (((~![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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4921,plain,
% 1.53/1.78 ((~![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))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(4922,plain,
% 1.53/1.78 ((~![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)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4921, 4920])).
% 1.53/1.78 tff(4923,plain,
% 1.53/1.78 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4922, 141, 572, 4919])).
% 1.53/1.78 tff(4924,plain,
% 1.53/1.78 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2091, 32, 4923])).
% 1.53/1.78 tff(4925,plain,
% 1.53/1.78 (b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4924, 2081])).
% 1.53/1.78 tff(4926,plain,
% 1.53/1.78 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[577, 4919, 572])).
% 1.53/1.78 tff(4927,plain,
% 1.53/1.78 (b(s(s(s(elem!1))), s(elem!1))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[353, 4926, 11])).
% 1.53/1.78 tff(4928,plain,
% 1.53/1.78 (((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~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)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4929,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4928])).
% 1.53/1.78 tff(4930,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4929, 4506])).
% 1.53/1.78 tff(4931,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(4932,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4931, 4930])).
% 1.53/1.78 tff(4933,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4932, 245, 4105, 4186, 2824])).
% 1.53/1.78 tff(4934,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2558, 4933])).
% 1.53/1.78 tff(4935,plain,
% 1.53/1.78 ((s(s(elem!1)) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4881])).
% 1.53/1.78 tff(4936,plain,
% 1.53/1.78 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4935, 686])).
% 1.53/1.78 tff(4937,plain,
% 1.53/1.78 ((elem!1 = s(s(s(z)))) <=> (s(s(elem!1)) = elem!1)),
% 1.53/1.78 inference(symmetry,[status(thm)],[4936])).
% 1.53/1.78 tff(4938,plain,
% 1.53/1.78 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4937])).
% 1.53/1.78 tff(4939,plain,
% 1.53/1.78 (~(s(s(elem!1)) = elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4887, 4938])).
% 1.53/1.78 tff(4940,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4941,plain,
% 1.53/1.78 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4942,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4941])).
% 1.53/1.78 tff(4943,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4942, 4940])).
% 1.53/1.78 tff(4944,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(4945,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 1.53/1.78 tff(4946,plain,
% 1.53/1.78 (~b(s(s(s(elem!1))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4945, 245, 1287, 2939, 838])).
% 1.53/1.78 tff(4947,plain,
% 1.53/1.78 (r(s(s(s(elem!1))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[37, 4946])).
% 1.53/1.78 tff(4948,plain,
% 1.53/1.78 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4177, 141, 4947, 106])).
% 1.53/1.78 tff(4949,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1320, 4948, 1312])).
% 1.53/1.78 tff(4950,plain,
% 1.53/1.78 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1801, 245, 1287, 2939, 4949])).
% 1.53/1.78 tff(4951,plain,
% 1.53/1.78 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1263, 4950, 1])).
% 1.53/1.78 tff(4952,plain,
% 1.53/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4953,plain,
% 1.53/1.78 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(4954,plain,
% 1.53/1.78 (((~![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(elem!1), z)) | (~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), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[4953])).
% 1.53/1.78 tff(4955,plain,
% 1.53/1.78 (((~![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(elem!1), z)) | (~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), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[4954, 4952])).
% 1.53/1.78 tff(4956,plain,
% 1.53/1.78 ((~![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(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(4957,plain,
% 1.53/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[4956, 4955])).
% 1.53/1.78 tff(4958,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4957, 141, 1097, 1366, 106])).
% 1.53/1.78 tff(4959,plain,((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(4960,plain,
% 1.53/1.78 (~r(s(elem!1), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4959, 4951, 106])).
% 1.53/1.78 tff(4961,plain,
% 1.53/1.78 (b(s(elem!1), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1039, 4960])).
% 1.53/1.78 tff(4962,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.78 tff(4963,plain,
% 1.53/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4964,plain,
% 1.53/1.79 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4965,plain,
% 1.53/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[4964])).
% 1.53/1.79 tff(4966,plain,
% 1.53/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[4965, 4963])).
% 1.53/1.79 tff(4967,plain,
% 1.53/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(4968,plain,
% 1.53/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[4967, 4966])).
% 1.53/1.79 tff(4969,plain,
% 1.53/1.79 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4968, 141, 1366])).
% 1.53/1.79 tff(4970,plain,
% 1.53/1.79 (~r(s(elem!1), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4969, 4962])).
% 1.53/1.79 tff(4971,plain,
% 1.53/1.79 (b(s(elem!1), s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[484, 32, 481, 4970])).
% 1.53/1.79 tff(4972,plain,
% 1.53/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4973,plain,
% 1.53/1.79 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4974,plain,
% 1.53/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[4973])).
% 1.53/1.79 tff(4975,plain,
% 1.53/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[4974, 4972])).
% 1.53/1.79 tff(4976,plain,
% 1.53/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(4977,plain,
% 1.53/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[4976, 4975])).
% 1.53/1.79 tff(4978,plain,
% 1.53/1.79 ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4977, 141, 310])).
% 1.53/1.79 tff(4979,plain,
% 1.53/1.79 (~r(s(s(elem!1)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4978, 4962])).
% 1.53/1.79 tff(4980,plain,
% 1.53/1.79 (b(s(s(elem!1)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[542, 32, 258, 4979])).
% 1.53/1.79 tff(4981,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4982,plain,
% 1.53/1.79 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4983,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X0, 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), s(s(elem!1))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[4982])).
% 1.53/1.79 tff(4984,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~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(X0, 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), s(s(elem!1)))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[4983, 4981])).
% 1.53/1.79 tff(4985,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(4986,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[4985, 4984])).
% 1.53/1.79 tff(4987,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4986, 245, 288, 838, 4980, 4971])).
% 1.53/1.79 tff(4988,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(4989,plain,
% 1.53/1.79 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4988, 4961, 838, 481, 4951, 310])).
% 1.53/1.79 tff(4990,plain,
% 1.53/1.79 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[4989, 4897])).
% 1.53/1.79 tff(4991,plain,
% 1.53/1.79 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1515, 4990])).
% 1.53/1.79 tff(4992,plain,
% 1.53/1.79 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[4991, 4892])).
% 1.53/1.79 tff(4993,plain,
% 1.53/1.79 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[4992, 4891])).
% 1.53/1.79 tff(4994,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4995,plain,
% 1.53/1.79 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(4996,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[4995])).
% 1.53/1.79 tff(4997,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[4996, 4994])).
% 1.53/1.79 tff(4998,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(4999,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 1.53/1.79 tff(5000,plain,
% 1.53/1.79 (~b(z, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4999, 245, 1287, 2939, 838])).
% 1.53/1.79 tff(5001,plain,
% 1.53/1.79 (r(z, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[197, 5000])).
% 1.53/1.79 tff(5002,plain,
% 1.53/1.79 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3360, 5001, 310])).
% 1.53/1.79 tff(5003,plain,
% 1.53/1.79 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1239, 5002, 1304])).
% 1.53/1.79 tff(5004,plain,
% 1.53/1.79 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[2898])).
% 1.53/1.79 tff(5005,plain,
% 1.53/1.79 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[5004, 61])).
% 1.53/1.79 tff(5006,plain,
% 1.53/1.79 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5005])).
% 1.53/1.79 tff(5007,plain,
% 1.53/1.79 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[209, 5006])).
% 1.53/1.79 tff(5008,plain,
% 1.53/1.79 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2837, 4951, 572])).
% 1.53/1.79 tff(5009,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1432, 5008, 5007])).
% 1.53/1.79 tff(5010,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5011,plain,
% 1.53/1.79 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5012,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5011])).
% 1.53/1.79 tff(5013,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[5012, 5010])).
% 1.53/1.79 tff(5014,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(5015,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 1.53/1.79 tff(5016,plain,
% 1.53/1.79 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5015, 245, 5009, 2824, 5003, 4993])).
% 1.53/1.79 tff(5017,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.53/1.79 tff(5018,plain,
% 1.53/1.79 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[523, 32, 5017, 5016])).
% 1.53/1.79 tff(5019,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5020,plain,
% 1.53/1.79 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(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(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5021,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5020])).
% 1.53/1.79 tff(5022,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[5021, 5019])).
% 1.53/1.79 tff(5023,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(5024,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5023, 5022])).
% 1.53/1.79 tff(5025,plain,
% 1.53/1.79 ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5024, 245, 4186, 2824, 5003])).
% 1.53/1.79 tff(5026,plain,
% 1.53/1.79 (~b(elem!1, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5025, 5009])).
% 1.53/1.79 tff(5027,plain,
% 1.53/1.79 (r(elem!1, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1724, 5026, 1673])).
% 1.53/1.79 tff(5028,plain,
% 1.53/1.79 (((~![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)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5029,plain,
% 1.53/1.79 ((~![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)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(5030,plain,
% 1.53/1.79 ((~![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))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5029, 5028])).
% 1.53/1.79 tff(5031,plain,
% 1.53/1.79 (~r(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5030, 141, 5027, 5018])).
% 1.53/1.79 tff(5032,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5033,plain,
% 1.53/1.79 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5034,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5033])).
% 1.53/1.79 tff(5035,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[5034, 5032])).
% 1.53/1.79 tff(5036,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(5037,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 1.53/1.79 tff(5038,plain,
% 1.53/1.79 (~b(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5037, 245, 5009, 2824, 4993])).
% 1.53/1.79 tff(5039,plain,
% 1.53/1.79 (((~![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))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5040,plain,
% 1.53/1.79 ((~![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))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(5041,plain,
% 1.53/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[5040, 5039])).
% 1.53/1.79 tff(5042,plain,
% 1.53/1.79 ((s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5041, 32, 5038])).
% 1.53/1.79 tff(5043,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5042, 5031, 4939])).
% 1.53/1.79 tff(5044,plain,((~b(z, s(elem!1))) | (~(s(z) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(5045,plain,
% 1.53/1.79 (~b(z, s(elem!1))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5044, 4905, 520, 2824, 397, 2898, 4186, 572, 4934, 1, 4927, 4925])).
% 1.53/1.79 tff(5046,plain,
% 1.53/1.79 (r(z, s(elem!1))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[644, 5045])).
% 1.53/1.79 tff(5047,plain,
% 1.53/1.79 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3674, 5046, 4905])).
% 1.53/1.79 tff(5048,plain,
% 1.53/1.79 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[420, 5047, 7])).
% 1.53/1.79 tff(5049,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3580, 141, 1342, 310, 1366])).
% 1.53/1.79 tff(5050,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(5051,plain,
% 1.53/1.79 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5050, 5046, 4905])).
% 1.53/1.79 tff(5052,plain,
% 1.53/1.79 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1263, 5051, 1])).
% 1.53/1.79 tff(5053,plain,
% 1.53/1.79 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1295, 5052, 4927, 5048])).
% 1.53/1.79 tff(5054,plain,
% 1.53/1.79 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1239, 5053, 1304])).
% 1.53/1.79 tff(5055,plain,
% 1.53/1.79 (~r(s(s(elem!1)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4977, 141, 310, 4962])).
% 1.53/1.79 tff(5056,plain,
% 1.53/1.79 (b(s(s(elem!1)), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[542, 32, 258, 5055])).
% 1.53/1.79 tff(5057,plain,
% 1.53/1.79 (((~![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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5058,plain,
% 1.53/1.79 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(5059,plain,
% 1.53/1.79 (((~![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(elem!1)), s(s(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[5058])).
% 1.53/1.80 tff(5060,plain,
% 1.53/1.80 (((~![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(elem!1)), s(s(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(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.80 inference(transitivity,[status(thm)],[5059, 5057])).
% 1.53/1.80 tff(5061,plain,
% 1.53/1.80 ((~![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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.53/1.80 inference(quant_inst,[status(thm)],[])).
% 1.53/1.80 tff(5062,plain,
% 1.53/1.80 ((~![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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[5061, 5060])).
% 1.53/1.80 tff(5063,plain,
% 1.53/1.80 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[5062, 141, 407, 4962])).
% 1.53/1.80 tff(5064,plain,
% 1.53/1.80 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[523, 32, 5017, 5063])).
% 1.53/1.80 tff(5065,plain,
% 1.53/1.80 (~r(z, s(s(s(elem!1))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3360, 407, 310])).
% 1.53/1.80 tff(5066,plain,
% 1.53/1.80 (b(z, s(s(s(elem!1))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[197, 5065])).
% 1.53/1.80 tff(5067,plain,
% 1.53/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(5068,plain,
% 1.53/1.80 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(5069,plain,
% 1.53/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[5068])).
% 1.53/1.80 tff(5070,plain,
% 1.53/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[5069, 5067])).
% 1.63/1.80 tff(5071,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(5072,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5071, 5070])).
% 1.63/1.80 tff(5073,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5072, 245, 1287, 2939, 5066, 5064, 5056])).
% 1.63/1.80 tff(5074,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(5075,plain,
% 1.63/1.80 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5074, 4927, 4925, 520, 5054, 4905])).
% 1.63/1.80 tff(5076,plain,
% 1.63/1.80 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5075, 4897])).
% 1.63/1.80 tff(5077,plain,
% 1.63/1.80 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1515, 5076])).
% 1.63/1.80 tff(5078,plain,
% 1.63/1.80 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5077, 4892])).
% 1.63/1.80 tff(5079,plain,
% 1.63/1.80 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5078, 4891])).
% 1.63/1.80 tff(5080,plain,
% 1.63/1.80 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3538, 5054, 4919])).
% 1.63/1.80 tff(5081,plain,
% 1.63/1.80 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1432, 5080, 5007])).
% 1.63/1.80 tff(5082,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5083,plain,
% 1.63/1.80 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5084,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5083])).
% 1.63/1.80 tff(5085,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[5084, 5082])).
% 1.63/1.80 tff(5086,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(5087,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 1.63/1.80 tff(5088,plain,
% 1.63/1.80 (~b(elem!1, s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5087, 245, 4186, 5081, 2824, 5079])).
% 1.63/1.80 tff(5089,plain,
% 1.63/1.80 (~b(elem!1, s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5088, 4889])).
% 1.63/1.80 tff(5090,plain,
% 1.63/1.80 (r(elem!1, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[967, 5089, 4887])).
% 1.63/1.80 tff(5091,plain,
% 1.63/1.80 (r(elem!1, s(s(elem!1)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5090, 4883])).
% 1.63/1.80 tff(5092,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5093,plain,
% 1.63/1.80 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5094,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5093])).
% 1.63/1.80 tff(5095,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[5094, 5092])).
% 1.63/1.80 tff(5096,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(5097,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5096, 5095])).
% 1.63/1.80 tff(5098,plain,
% 1.63/1.80 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5097, 245, 5081, 2824, 5052, 5079])).
% 1.63/1.80 tff(5099,plain,
% 1.63/1.80 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[484, 32, 397, 5098])).
% 1.63/1.80 tff(5100,plain,
% 1.63/1.80 (~b(elem!1, s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3866, 5052, 2824, 5048])).
% 1.63/1.80 tff(5101,plain,
% 1.63/1.80 (r(elem!1, s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2777, 5100, 2563])).
% 1.63/1.80 tff(5102,plain,
% 1.63/1.80 (((~![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(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(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5103,plain,
% 1.63/1.80 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5104,plain,
% 1.63/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5103])).
% 1.63/1.80 tff(5105,plain,
% 1.63/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[5104, 5102])).
% 1.63/1.80 tff(5106,plain,
% 1.63/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(5107,plain,
% 1.63/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5106, 5105])).
% 1.63/1.80 tff(5108,plain,
% 1.63/1.80 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5107, 141, 5101, 5099])).
% 1.63/1.80 tff(5109,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5108, 5091])).
% 1.63/1.80 tff(5110,plain,((~b(elem!1, z)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(5111,plain,
% 1.63/1.80 (~b(elem!1, z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5110, 2898, 4880, 1, 572, 11, 4105])).
% 1.63/1.80 tff(5112,plain,
% 1.63/1.80 (r(elem!1, z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[128, 5111, 3641])).
% 1.63/1.80 tff(5113,plain,
% 1.63/1.80 (~r(elem!1, s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[4639, 1342, 131])).
% 1.63/1.80 tff(5114,plain,
% 1.63/1.80 (b(elem!1, s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2777, 5113, 2563])).
% 1.63/1.80 tff(5115,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5116,plain,
% 1.63/1.80 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5117,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5116])).
% 1.63/1.80 tff(5118,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[5117, 5115])).
% 1.63/1.80 tff(5119,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(5120,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 1.63/1.80 tff(5121,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5120, 245, 4105, 1103, 2197, 2824, 556])).
% 1.63/1.80 tff(5122,plain,((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(5123,plain,
% 1.63/1.80 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5122, 2197, 1103, 4105, 2824])).
% 1.63/1.80 tff(5124,plain,
% 1.63/1.80 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1263, 5123, 1])).
% 1.63/1.80 tff(5125,plain,
% 1.63/1.80 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2837, 5124, 572])).
% 1.63/1.80 tff(5126,plain,
% 1.63/1.80 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1432, 5125, 399])).
% 1.63/1.80 tff(5127,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5128,plain,
% 1.63/1.80 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(5129,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5128])).
% 1.63/1.80 tff(5130,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[5129, 5127])).
% 1.63/1.80 tff(5131,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(5132,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[5131, 5130])).
% 1.63/1.80 tff(5133,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5132, 245, 4105, 5126, 2197, 2824])).
% 1.63/1.80 tff(5134,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(5135,plain,
% 1.63/1.80 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5134, 5114, 2824, 399, 572, 1, 4105])).
% 1.63/1.80 tff(5136,plain,
% 1.63/1.80 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1992, 5135])).
% 1.63/1.80 tff(5137,plain,
% 1.63/1.80 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3674, 5136, 1342])).
% 1.63/1.80 tff(5138,plain,
% 1.63/1.80 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[420, 5137, 7])).
% 1.63/1.80 tff(5139,plain,
% 1.63/1.80 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5050, 5136, 1342])).
% 1.63/1.81 tff(5140,plain,
% 1.63/1.81 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1263, 5139, 1])).
% 1.63/1.81 tff(5141,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3866, 5140, 5138, 2824, 5114])).
% 1.63/1.81 tff(5142,plain,((~r(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5143,plain,
% 1.63/1.81 (~r(z, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5142, 4880, 1, 5007, 572, 4105, 5112])).
% 1.63/1.81 tff(5144,plain,
% 1.63/1.81 (b(z, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[644, 5143])).
% 1.63/1.81 tff(5145,plain,
% 1.63/1.81 (r(s(z), z) <=> r(elem!1, z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2898])).
% 1.63/1.81 tff(5146,plain,
% 1.63/1.81 (r(elem!1, z) <=> r(s(z), z)),
% 1.63/1.81 inference(symmetry,[status(thm)],[5145])).
% 1.63/1.81 tff(5147,plain,
% 1.63/1.81 (r(s(z), z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5112, 5146])).
% 1.63/1.81 tff(5148,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2898])).
% 1.63/1.81 tff(5149,plain,
% 1.63/1.81 (b(z, s(z)) <=> b(z, elem!1)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2898])).
% 1.63/1.81 tff(5150,plain,
% 1.63/1.81 (b(z, elem!1) <=> b(z, s(z))),
% 1.63/1.81 inference(symmetry,[status(thm)],[5149])).
% 1.63/1.81 tff(5151,plain,
% 1.63/1.81 (b(z, s(z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[4105, 5150])).
% 1.63/1.81 tff(5152,plain,
% 1.63/1.81 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1432, 2838, 5007])).
% 1.63/1.81 tff(5153,plain,
% 1.63/1.81 (b(s(z), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[2898])).
% 1.63/1.81 tff(5154,plain,
% 1.63/1.81 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(symmetry,[status(thm)],[5153])).
% 1.63/1.81 tff(5155,plain,
% 1.63/1.81 (b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1390, 5154])).
% 1.63/1.81 tff(5156,assumption,(~b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.81 tff(5157,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5156, 5155])).
% 1.63/1.81 tff(5158,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(elem!1))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5159,plain,
% 1.63/1.81 (b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5158, 5152, 2898])).
% 1.63/1.81 tff(5160,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5161,plain,
% 1.63/1.81 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5162,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[5161])).
% 1.63/1.81 tff(5163,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[5162, 5160])).
% 1.63/1.81 tff(5164,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(5165,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 1.63/1.81 tff(5166,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5165, 245, 1943, 4187, 2653, 3380])).
% 1.63/1.81 tff(5167,plain,((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5168,plain,
% 1.63/1.81 (~b(s(s(s(s(elem!1)))), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5167, 5159, 5151, 2653])).
% 1.63/1.81 tff(5169,plain,
% 1.63/1.81 (r(s(s(s(s(elem!1)))), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2558, 5168])).
% 1.63/1.81 tff(5170,plain,
% 1.63/1.81 (~r(s(elem!1), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4959, 5169, 1366])).
% 1.63/1.81 tff(5171,plain,
% 1.63/1.81 (b(s(elem!1), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1039, 5170])).
% 1.63/1.81 tff(5172,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2853, 5152, 102, 1366, 2824, 1309, 572])).
% 1.63/1.81 tff(5173,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[353, 5172, 11])).
% 1.63/1.81 tff(5174,plain,
% 1.63/1.81 (~b(s(s(s(elem!1))), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2871, 245, 5173, 5171, 838])).
% 1.63/1.81 tff(5175,plain,
% 1.63/1.81 (r(s(s(s(elem!1))), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[37, 5174])).
% 1.63/1.81 tff(5176,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2177, 5175, 220])).
% 1.63/1.81 tff(5177,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[265, 5176])).
% 1.63/1.81 tff(5178,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5177, 5148])).
% 1.63/1.81 tff(5179,plain,
% 1.63/1.81 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5180,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[5179])).
% 1.63/1.81 tff(5181,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[5180, 5127])).
% 1.63/1.81 tff(5182,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(5183,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5182, 5181])).
% 1.63/1.81 tff(5184,plain,
% 1.63/1.81 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5183, 245, 4105, 5152, 2824])).
% 1.63/1.81 tff(5185,plain,
% 1.63/1.81 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1992, 5184])).
% 1.63/1.81 tff(5186,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), z)) | (~b(z, 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(X0, 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), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5187,plain,
% 1.63/1.81 (((~b(z, elem!1)) | (~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(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5188,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(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(X0, 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), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[5187])).
% 1.63/1.81 tff(5189,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(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(X0, 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), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[5188, 5186])).
% 1.63/1.81 tff(5190,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(5191,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5190, 5189])).
% 1.63/1.81 tff(5192,plain,
% 1.63/1.81 (~b(z, s(s(s(elem!1))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5191, 245, 4105, 5173, 5171, 838])).
% 1.63/1.81 tff(5193,plain,
% 1.63/1.81 (r(z, s(s(s(elem!1))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[197, 5192])).
% 1.63/1.81 tff(5194,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3360, 5193, 5185])).
% 1.63/1.81 tff(5195,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1239, 5194, 1309])).
% 1.63/1.81 tff(5196,plain,
% 1.63/1.81 (~b(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2849, 5195, 2824, 5152])).
% 1.63/1.81 tff(5197,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5196, 5178])).
% 1.63/1.81 tff(5198,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5199,plain,
% 1.63/1.81 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5198, 2898, 4880, 1304, 5147, 5144, 4105, 11, 4879, 96, 572])).
% 1.63/1.81 tff(5200,plain,
% 1.63/1.81 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1263, 5199, 1])).
% 1.63/1.81 tff(5201,plain,
% 1.63/1.81 (~b(elem!1, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5122, 2197, 556, 4105, 2824])).
% 1.63/1.81 tff(5202,plain,
% 1.63/1.81 (r(elem!1, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2777, 5201, 2774])).
% 1.63/1.81 tff(5203,plain,
% 1.63/1.81 (~r(s(elem!1), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1082, 5202, 131])).
% 1.63/1.81 tff(5204,plain,
% 1.63/1.81 (b(s(elem!1), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1039, 5203])).
% 1.63/1.81 tff(5205,plain,
% 1.63/1.81 (~b(s(s(s(s(elem!1)))), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3304, 5204, 838, 556])).
% 1.63/1.81 tff(5206,plain,
% 1.63/1.81 (r(s(s(s(s(elem!1)))), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2558, 5205])).
% 1.63/1.81 tff(5207,plain,
% 1.63/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5208,plain,
% 1.63/1.81 (((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5209,plain,
% 1.63/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[5208])).
% 1.63/1.81 tff(5210,plain,
% 1.63/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[5209, 5207])).
% 1.63/1.81 tff(5211,plain,
% 1.63/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(5212,plain,
% 1.63/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5211, 5210])).
% 1.63/1.81 tff(5213,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5212, 141, 131, 1368, 106])).
% 1.63/1.81 tff(5214,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5215,plain,
% 1.63/1.81 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5214, 5206, 131])).
% 1.63/1.81 tff(5216,plain,
% 1.63/1.81 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1432, 5215, 399])).
% 1.63/1.81 tff(5217,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5132, 245, 4105, 5216, 2197, 2824])).
% 1.63/1.81 tff(5218,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5219,plain,
% 1.63/1.81 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5218, 4880, 4105, 5007, 5112, 5144, 5200, 2563])).
% 1.63/1.81 tff(5220,plain,
% 1.63/1.81 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1992, 5219])).
% 1.63/1.81 tff(5221,plain,
% 1.63/1.81 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4818, 5219, 5112, 4105])).
% 1.63/1.81 tff(5222,plain,
% 1.63/1.81 (~b(elem!1, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3704, 245, 5221, 4880, 5200])).
% 1.63/1.81 tff(5223,plain,
% 1.63/1.81 (r(elem!1, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2777, 5222, 2563])).
% 1.63/1.81 tff(5224,plain,
% 1.63/1.81 (~r(s(elem!1), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1082, 5223, 5112])).
% 1.63/1.81 tff(5225,plain,
% 1.63/1.81 (b(s(elem!1), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1039, 5224])).
% 1.63/1.81 tff(5226,plain,
% 1.63/1.81 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[299, 245, 5066, 3528, 288])).
% 1.63/1.81 tff(5227,plain,
% 1.63/1.81 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[353, 5226, 11])).
% 1.63/1.81 tff(5228,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[577, 5227, 572])).
% 1.63/1.81 tff(5229,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[110, 5228, 102])).
% 1.63/1.81 tff(5230,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5231,plain,
% 1.63/1.81 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5232,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[5231])).
% 1.63/1.81 tff(5233,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[5232, 5230])).
% 1.63/1.81 tff(5234,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(5235,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5234, 5233])).
% 1.63/1.81 tff(5236,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5235, 245, 4105, 1390, 5229, 5066, 2824])).
% 1.63/1.81 tff(5237,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5238,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5237, 5221, 4105, 4880, 96, 572, 11, 5225, 5220])).
% 1.63/1.81 tff(5239,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1239, 5238, 1304])).
% 1.63/1.81 tff(5240,plain,
% 1.63/1.81 (~b(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2849, 5239, 4880, 5221])).
% 1.63/1.81 tff(5241,plain,
% 1.63/1.81 (r(s(s(s(elem!1))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[110, 5240, 96])).
% 1.63/1.81 tff(5242,plain,
% 1.63/1.81 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[577, 5241, 572])).
% 1.63/1.81 tff(5243,plain,
% 1.63/1.81 (b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[353, 5242, 11])).
% 1.63/1.81 tff(5244,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5245,plain,
% 1.63/1.81 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(5246,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[5245])).
% 1.63/1.81 tff(5247,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[5246, 5244])).
% 1.63/1.81 tff(5248,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(5249,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5248, 5247])).
% 1.63/1.81 tff(5250,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5249, 245, 5243, 5221, 4880, 5200, 5239])).
% 1.63/1.81 tff(5251,plain,((~(s(z) = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (elem!1 = z) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(5252,plain,
% 1.63/1.81 (~(s(z) = elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5251, 4105, 1277, 11, 1, 124, 4872])).
% 1.63/1.81 tff(5253,plain,
% 1.63/1.81 (b(s(z), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[389, 5252, 4494])).
% 1.63/1.81 tff(5254,plain,
% 1.63/1.81 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[338])).
% 1.63/1.81 tff(5255,plain,
% 1.63/1.81 (~(elem!1 = s(z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[5252, 5254])).
% 1.63/1.81 tff(5256,plain,
% 1.63/1.81 (~r(elem!1, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4791, 5255, 564, 2562, 1, 4105, 9, 11, 5253])).
% 1.63/1.81 tff(5257,plain,
% 1.63/1.81 (b(elem!1, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2777, 5256, 2563])).
% 1.63/1.81 tff(5258,plain,
% 1.63/1.81 (~b(elem!1, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4840, 5257, 5253, 4105, 1, 564, 2562, 9, 11])).
% 1.63/1.81 tff(5259,plain,
% 1.63/1.81 (r(elem!1, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[281, 5258, 5255])).
% 1.63/1.81 tff(5260,plain,
% 1.63/1.81 (~r(s(elem!1), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4206, 5259, 1277])).
% 1.63/1.81 tff(5261,plain,
% 1.63/1.81 (b(s(elem!1), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[369, 5260, 348])).
% 1.63/1.81 tff(5262,plain,
% 1.63/1.81 (~b(s(z), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4850, 245, 5257, 5261, 5253])).
% 1.63/1.81 tff(5263,plain,
% 1.63/1.81 (r(s(z), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[440, 5262, 9])).
% 1.63/1.81 tff(5264,plain,
% 1.63/1.81 (~b(z, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4858, 245, 4105, 5257, 5261, 5253])).
% 1.63/1.81 tff(5265,plain,
% 1.63/1.81 (r(z, s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[644, 5264])).
% 1.63/1.81 tff(5266,plain,
% 1.63/1.81 (~r(z, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[2403, 141, 5265, 5263])).
% 1.63/1.81 tff(5267,plain,
% 1.63/1.81 (b(z, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1421, 5266])).
% 1.63/1.81 tff(5268,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4868, 245, 4105, 5257, 5261, 5253, 5267])).
% 1.63/1.81 tff(5269,plain,((~b(z, elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | r(s(z), elem!1) | r(s(s(s(s(s(z))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(5270,plain,
% 1.63/1.82 (r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5269, 4470, 1, 564, 2562, 2569, 4102, 9])).
% 1.63/1.82 tff(5271,plain,
% 1.63/1.82 (r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5270, 4493])).
% 1.63/1.82 tff(5272,plain,
% 1.63/1.82 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4310, 5271, 4491, 4488, 2699, 4485, 4482])).
% 1.63/1.82 tff(5273,plain,
% 1.63/1.82 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1820, 5272])).
% 1.63/1.82 tff(5274,plain,
% 1.63/1.82 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5273, 4472])).
% 1.63/1.82 tff(5275,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5276,plain,
% 1.63/1.82 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5277,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5276])).
% 1.63/1.82 tff(5278,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[5277, 5275])).
% 1.63/1.82 tff(5279,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(5280,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5279, 5278])).
% 1.63/1.82 tff(5281,plain,
% 1.63/1.82 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5280, 245, 4102, 4401, 2573, 5274])).
% 1.63/1.82 tff(5282,plain,
% 1.63/1.82 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2156, 4491, 1])).
% 1.63/1.82 tff(5283,plain,
% 1.63/1.82 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2163, 5282])).
% 1.63/1.82 tff(5284,plain,
% 1.63/1.82 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2914, 5283, 4471])).
% 1.63/1.82 tff(5285,plain,
% 1.63/1.82 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2517, 32, 5284, 5281])).
% 1.63/1.82 tff(5286,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5287,plain,
% 1.63/1.82 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5288,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5287])).
% 1.63/1.82 tff(5289,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.63/1.82 inference(transitivity,[status(thm)],[5288, 5286])).
% 1.63/1.82 tff(5290,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(5291,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 1.63/1.82 tff(5292,plain,
% 1.63/1.82 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5291, 245, 4102, 4401, 5274])).
% 1.63/1.82 tff(5293,plain,
% 1.63/1.82 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2220, 32, 1554, 5292])).
% 1.63/1.82 tff(5294,plain,
% 1.63/1.82 (((~![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(s(s(elem!1)))))), z)) | (~r(s(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(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5295,plain,
% 1.63/1.82 ((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(5296,plain,
% 1.63/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 1.63/1.82 tff(5297,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5296, 141, 4411, 5293, 5285])).
% 1.63/1.82 tff(5298,plain,(b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(5299,plain,
% 1.63/1.82 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5298, 9, 564, 2562, 1])).
% 1.63/1.82 tff(5300,plain,
% 1.63/1.82 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1432, 3539, 2568])).
% 1.63/1.82 tff(5301,plain,
% 1.63/1.82 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5183, 245, 4102, 5300, 5299])).
% 1.63/1.82 tff(5302,plain,
% 1.63/1.82 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1992, 5301])).
% 1.63/1.82 tff(5303,plain,
% 1.63/1.82 (~b(s(elem!1), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5237, 5302, 4102, 5299, 96, 1277, 2569, 407, 5300])).
% 1.63/1.82 tff(5304,plain,
% 1.63/1.82 (r(s(elem!1), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1039, 5303])).
% 1.63/1.82 tff(5305,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3588, 141, 1097, 310, 1366])).
% 1.63/1.82 tff(5306,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(5307,plain,
% 1.63/1.82 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5306, 5304, 5302])).
% 1.63/1.82 tff(5308,plain,
% 1.63/1.82 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1263, 5307, 1])).
% 1.63/1.82 tff(5309,plain,
% 1.63/1.82 (~b(elem!1, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3704, 245, 5300, 5299, 5308])).
% 1.63/1.82 tff(5310,plain,
% 1.63/1.82 (r(elem!1, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2777, 5309, 2563])).
% 1.63/1.82 tff(5311,plain,
% 1.63/1.82 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4922, 141, 1277, 170])).
% 1.63/1.82 tff(5312,plain,
% 1.63/1.82 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2091, 32, 5311])).
% 1.63/1.82 tff(5313,plain,
% 1.63/1.82 (b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5312, 2888])).
% 1.63/1.82 tff(5314,plain,
% 1.63/1.82 (b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[353, 3511, 2569])).
% 1.63/1.82 tff(5315,plain,
% 1.63/1.82 (~r(s(z), s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1143, 619, 170])).
% 1.63/1.82 tff(5316,plain,
% 1.63/1.82 (b(s(z), s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1133, 5315])).
% 1.63/1.82 tff(5317,plain,
% 1.63/1.82 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5318,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5317])).
% 1.63/1.82 tff(5319,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[5318, 4418])).
% 1.63/1.82 tff(5320,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(5321,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5320, 5319])).
% 1.63/1.82 tff(5322,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5321, 245, 1287, 2939, 626, 5316])).
% 1.63/1.82 tff(5323,plain,((~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(5324,plain,
% 1.63/1.82 (~r(s(z), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5323, 5314, 5313, 9, 170, 1277])).
% 1.63/1.82 tff(5325,plain,
% 1.63/1.82 (~r(z, s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3360, 5302, 407])).
% 1.63/1.82 tff(5326,plain,
% 1.63/1.82 (b(z, s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[197, 5325])).
% 1.63/1.82 tff(5327,plain,
% 1.63/1.82 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5328,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5327])).
% 1.63/1.82 tff(5329,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[5328, 4994])).
% 1.63/1.82 tff(5330,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(5331,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5330, 5329])).
% 1.63/1.82 tff(5332,plain,
% 1.63/1.82 (~b(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5331, 245, 5314, 5313, 5326])).
% 1.63/1.82 tff(5333,plain,
% 1.63/1.82 (r(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[644, 5332])).
% 1.63/1.82 tff(5334,plain,
% 1.63/1.82 (~r(elem!1, z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5142, 5333, 1, 2568, 1277, 4102, 5299])).
% 1.63/1.82 tff(5335,plain,
% 1.63/1.82 (b(elem!1, z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[128, 5334, 124])).
% 1.63/1.82 tff(5336,plain,
% 1.63/1.82 (~(s(z) = elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5110, 5335, 5299, 1, 1277, 2569, 4102])).
% 1.63/1.82 tff(5337,plain,
% 1.63/1.82 (b(s(z), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[389, 5336, 5324])).
% 1.63/1.82 tff(5338,plain,
% 1.63/1.82 (elem!1 = s(z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4791, 5337, 564, 2562, 1, 4102, 9, 2569, 5310])).
% 1.63/1.82 tff(5339,plain,
% 1.63/1.82 (s(z) = elem!1),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5338, 339])).
% 1.63/1.82 tff(5340,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5336, 5339])).
% 1.63/1.82 tff(5341,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | b(s(elem!1), elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(5342,plain,
% 1.63/1.82 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5341, 170, 2562, 1, 9, 564])).
% 1.63/1.82 tff(5343,plain,
% 1.63/1.82 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1239, 5342, 1304])).
% 1.63/1.82 tff(5344,plain,
% 1.63/1.82 (~(s(z) = elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5110, 4186, 2824, 1, 572, 11, 4105])).
% 1.63/1.82 tff(5345,plain,
% 1.63/1.82 (b(s(z), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[389, 5344, 4494])).
% 1.63/1.82 tff(5346,plain,
% 1.63/1.82 (~b(z, s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4595, 5345, 4186, 4105])).
% 1.63/1.82 tff(5347,plain,
% 1.63/1.82 (r(z, s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1421, 5346])).
% 1.63/1.82 tff(5348,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5349,plain,
% 1.63/1.82 (((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5350,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5349])).
% 1.63/1.82 tff(5351,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[5350, 5348])).
% 1.63/1.82 tff(5352,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(5353,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5352, 5351])).
% 1.63/1.82 tff(5354,plain,
% 1.63/1.82 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5353, 245, 4105, 4186, 5345, 2824])).
% 1.63/1.82 tff(5355,plain,
% 1.63/1.82 (r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[217, 5354])).
% 1.63/1.82 tff(5356,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4226, 5355, 4934, 5347])).
% 1.63/1.82 tff(5357,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | r(s(z), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(5358,plain,
% 1.63/1.82 (~b(elem!1, z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5357, 5324, 5299, 4102, 1, 1277, 2569])).
% 1.63/1.82 tff(5359,plain,
% 1.63/1.82 (r(elem!1, z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[128, 5358, 124])).
% 1.63/1.82 tff(5360,plain,
% 1.63/1.82 (~r(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5142, 5359, 1, 2568, 1277, 4102, 5299])).
% 1.63/1.82 tff(5361,plain,
% 1.63/1.82 (b(z, s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[644, 5360])).
% 1.63/1.82 tff(5362,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5363,plain,
% 1.63/1.82 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5364,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5363])).
% 1.63/1.82 tff(5365,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[5364, 5362])).
% 1.63/1.82 tff(5366,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(5367,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[5366, 5365])).
% 1.63/1.82 tff(5368,plain,
% 1.63/1.82 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5367, 245, 4102, 5313, 5299, 5343])).
% 1.63/1.82 tff(5369,plain,
% 1.63/1.82 (~b(z, s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5368, 5361])).
% 1.63/1.82 tff(5370,plain,
% 1.63/1.82 (r(z, s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[197, 5369])).
% 1.63/1.82 tff(5371,plain,
% 1.63/1.82 (~r(elem!1, s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3608, 5370, 5359])).
% 1.63/1.82 tff(5372,plain,
% 1.63/1.82 (b(elem!1, s(s(s(elem!1))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1724, 5371, 1673])).
% 1.63/1.82 tff(5373,plain,
% 1.63/1.82 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1432, 2838, 399])).
% 1.63/1.82 tff(5374,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(elem!1)))), z)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5375,plain,
% 1.63/1.82 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, 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(elem!1)))), z)))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(5376,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(elem!1)))), z))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5375])).
% 1.63/1.82 tff(5377,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(elem!1)))), z)))),
% 1.63/1.83 inference(transitivity,[status(thm)],[5376, 5374])).
% 1.63/1.83 tff(5378,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(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)))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5379,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(elem!1)))), z))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5378, 5377])).
% 1.63/1.83 tff(5380,plain,
% 1.63/1.83 (~b(s(s(s(s(elem!1)))), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5379, 245, 4105, 5373, 2824])).
% 1.63/1.83 tff(5381,plain,
% 1.63/1.83 (r(s(s(s(s(elem!1)))), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2558, 5380])).
% 1.63/1.83 tff(5382,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5383,plain,
% 1.63/1.83 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5384,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5383])).
% 1.63/1.83 tff(5385,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[5384, 5382])).
% 1.63/1.83 tff(5386,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5387,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5386, 5385])).
% 1.63/1.83 tff(5388,plain,
% 1.63/1.83 (~b(elem!1, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5387, 245, 5373, 2824, 1276])).
% 1.63/1.83 tff(5389,plain,
% 1.63/1.83 (r(elem!1, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1724, 5388, 1673])).
% 1.63/1.83 tff(5390,plain,
% 1.63/1.83 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5183, 245, 4105, 5373, 2824])).
% 1.63/1.83 tff(5391,plain,
% 1.63/1.83 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1992, 5390])).
% 1.63/1.83 tff(5392,plain,
% 1.63/1.83 (~r(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5050, 5391, 1366])).
% 1.63/1.83 tff(5393,plain,
% 1.63/1.83 (b(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[644, 5392])).
% 1.63/1.83 tff(5394,plain,
% 1.63/1.83 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5367, 245, 4105, 2939, 2824, 1276])).
% 1.63/1.83 tff(5395,plain,
% 1.63/1.83 (~b(z, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5394, 5393])).
% 1.63/1.83 tff(5396,plain,
% 1.63/1.83 (r(z, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[197, 5395])).
% 1.63/1.83 tff(5397,plain,
% 1.63/1.83 (~r(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3608, 5396, 5389])).
% 1.63/1.83 tff(5398,plain,
% 1.63/1.83 (b(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[128, 5397, 3641])).
% 1.63/1.83 tff(5399,plain,
% 1.63/1.83 (~(s(z) = elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5110, 5398, 2824, 1, 572, 2338, 4105])).
% 1.63/1.83 tff(5400,plain,
% 1.63/1.83 (b(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[389, 5399, 4494])).
% 1.63/1.83 tff(5401,plain,
% 1.63/1.83 (~b(z, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4595, 5400, 5398, 4105])).
% 1.63/1.83 tff(5402,plain,
% 1.63/1.83 (r(z, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1421, 5401])).
% 1.63/1.83 tff(5403,plain,
% 1.63/1.83 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4226, 5402, 5381])).
% 1.63/1.83 tff(5404,plain,
% 1.63/1.83 (b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[217, 5403])).
% 1.63/1.83 tff(5405,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5353, 245, 4105, 5398, 5400, 2824, 5404])).
% 1.63/1.83 tff(5406,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | r(s(z), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (elem!1 = z) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5407,plain,
% 1.63/1.83 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5406, 5324, 5299, 4102, 1, 1277, 124, 5313, 5343, 2568])).
% 1.63/1.83 tff(5408,plain,
% 1.63/1.83 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1263, 5407, 1])).
% 1.63/1.83 tff(5409,plain,
% 1.63/1.83 (~b(z, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5218, 5361, 4102, 2568, 5299, 5359, 5408, 2563])).
% 1.63/1.83 tff(5410,plain,
% 1.63/1.83 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4818, 5409, 5359, 4102])).
% 1.63/1.83 tff(5411,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5387, 245, 5410, 5372, 5299, 5343])).
% 1.63/1.83 tff(5412,plain,((~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (s(z) = s(elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5413,plain,
% 1.63/1.83 (~r(s(s(s(elem!1))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5412, 9, 2562, 1, 564])).
% 1.63/1.83 tff(5414,plain,
% 1.63/1.83 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[110, 5413, 96])).
% 1.63/1.83 tff(5415,plain,
% 1.63/1.83 (~b(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4917, 5414, 4102, 1304, 5299])).
% 1.63/1.83 tff(5416,plain,
% 1.63/1.83 (r(elem!1, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[128, 5415, 124])).
% 1.63/1.83 tff(5417,plain,
% 1.63/1.83 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1432, 4802, 399])).
% 1.63/1.83 tff(5418,plain,
% 1.63/1.83 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2837, 5417, 572])).
% 1.63/1.83 tff(5419,plain,
% 1.63/1.83 (~r(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5142, 131, 1, 399, 572, 4105, 2824])).
% 1.63/1.83 tff(5420,plain,
% 1.63/1.83 (b(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[644, 5419])).
% 1.63/1.83 tff(5421,plain,
% 1.63/1.83 (b(z, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4818, 4802, 131, 4105])).
% 1.63/1.83 tff(5422,plain,
% 1.63/1.83 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5218, 5421, 4105, 399, 2824, 131, 5420, 2563])).
% 1.63/1.83 tff(5423,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1263, 5422, 5418, 1])).
% 1.63/1.83 tff(5424,plain,(b(elem!1, s(s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5425,plain,
% 1.63/1.83 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5424, 5299, 4102, 2568, 1, 5416, 1277])).
% 1.63/1.83 tff(5426,plain,
% 1.63/1.83 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[2849, 5425, 5299, 5414])).
% 1.63/1.83 tff(5427,plain,
% 1.63/1.83 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1239, 5426, 1304])).
% 1.63/1.83 tff(5428,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5235, 245, 4105, 1390, 1427, 235, 2824])).
% 1.63/1.83 tff(5429,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5430,plain,
% 1.63/1.83 (~b(z, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5429, 5425, 5414, 4102, 5299])).
% 1.63/1.83 tff(5431,plain,
% 1.63/1.83 (r(z, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[197, 5430])).
% 1.63/1.83 tff(5432,plain,
% 1.63/1.83 (~r(z, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3360, 5431, 5427])).
% 1.63/1.83 tff(5433,plain,
% 1.63/1.83 (b(z, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1992, 5432])).
% 1.63/1.83 tff(5434,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5132, 245, 4102, 5425, 5433, 5299])).
% 1.63/1.83 tff(5435,plain,((s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5436,plain,
% 1.63/1.83 (s(z) = s(elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5435, 2562, 1, 564])).
% 1.63/1.83 tff(5437,plain,
% 1.63/1.83 (z = elem!1),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[57, 5436])).
% 1.63/1.83 tff(5438,plain,
% 1.63/1.83 (elem!1 = z),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3643, 5437])).
% 1.63/1.83 tff(5439,plain,
% 1.63/1.83 (b(z, elem!1) <=> b(z, z)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5438])).
% 1.63/1.83 tff(5440,plain,
% 1.63/1.83 (b(z, z) <=> b(z, elem!1)),
% 1.63/1.83 inference(symmetry,[status(thm)],[5439])).
% 1.63/1.83 tff(5441,plain,
% 1.63/1.83 ((~b(z, z)) <=> (~b(z, elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5440])).
% 1.63/1.83 tff(5442,plain,
% 1.63/1.83 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5443,plain,
% 1.63/1.83 (~b(z, z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5442, 77])).
% 1.63/1.83 tff(5444,plain,
% 1.63/1.83 (~b(z, elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5443, 5441])).
% 1.63/1.83 tff(5445,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4102, 5444])).
% 1.63/1.83 tff(5446,plain,((s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5447,plain,
% 1.63/1.83 (s(s(s(s(elem!1)))) = elem!1),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5446, 564, 1])).
% 1.63/1.83 tff(5448,plain,
% 1.63/1.83 (s(s(z)) = s(s(s(elem!1)))),
% 1.63/1.83 inference(transitivity,[status(thm)],[586, 864, 113])).
% 1.63/1.83 tff(5449,plain,
% 1.63/1.83 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5448])).
% 1.63/1.83 tff(5450,plain,
% 1.63/1.83 (s(z) = s(s(s(s(s(s(elem!1))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[591, 5449, 157, 313])).
% 1.63/1.83 tff(5451,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[465, 5450])).
% 1.63/1.83 tff(5452,plain,((~(s(s(s(z))) = elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5453,plain,
% 1.63/1.83 (~(s(s(s(z))) = elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5452, 5447])).
% 1.63/1.83 tff(5454,plain,
% 1.63/1.83 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5447])).
% 1.63/1.83 tff(5455,plain,
% 1.63/1.83 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.63/1.83 inference(transitivity,[status(thm)],[5454, 339])).
% 1.63/1.83 tff(5456,plain,
% 1.63/1.83 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5455])).
% 1.63/1.83 tff(5457,plain,
% 1.63/1.83 (~(s(z) = elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[209, 5456])).
% 1.63/1.83 tff(5458,plain,
% 1.63/1.83 (b(s(s(s(s(elem!1)))), elem!1) <=> b(elem!1, elem!1)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[199])).
% 1.63/1.83 tff(5459,plain,
% 1.63/1.83 (b(elem!1, elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.83 inference(symmetry,[status(thm)],[5458])).
% 1.63/1.83 tff(5460,plain,
% 1.63/1.83 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5459])).
% 1.63/1.83 tff(5461,plain,
% 1.63/1.83 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[79, 5460])).
% 1.63/1.83 tff(5462,plain,
% 1.63/1.83 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = z)),
% 1.63/1.83 inference(monotonicity,[status(thm)],[199])).
% 1.63/1.83 tff(5463,plain,
% 1.63/1.83 ((s(s(s(s(elem!1)))) = z) <=> (z = elem!1)),
% 1.63/1.83 inference(transitivity,[status(thm)],[5462, 119])).
% 1.63/1.83 tff(5464,plain,
% 1.63/1.83 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = elem!1))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5463])).
% 1.63/1.83 tff(5465,plain,
% 1.63/1.83 (~(z = elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[66, 5464])).
% 1.63/1.83 tff(5466,plain,
% 1.63/1.83 (~(s(z) = s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[57, 5465])).
% 1.63/1.83 tff(5467,plain,
% 1.63/1.83 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1937, 90, 106, 8, 89, 1])).
% 1.63/1.83 tff(5468,plain,
% 1.63/1.83 ((~b(s(elem!1), elem!1)) <=> (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[307])).
% 1.63/1.83 tff(5469,plain,
% 1.63/1.83 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[564, 5468])).
% 1.63/1.83 tff(5470,plain,
% 1.63/1.83 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1263, 5469, 1])).
% 1.63/1.83 tff(5471,plain,
% 1.63/1.83 (~r(s(elem!1), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[649, 1277, 289])).
% 1.63/1.83 tff(5472,plain,
% 1.63/1.83 (b(s(elem!1), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1039, 5471])).
% 1.63/1.83 tff(5473,plain,
% 1.63/1.83 (~r(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[632, 141, 289, 1277])).
% 1.63/1.83 tff(5474,plain,
% 1.63/1.83 (b(z, s(elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[644, 5473])).
% 1.63/1.83 tff(5475,plain,
% 1.63/1.83 (~r(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[670, 1277, 289, 9])).
% 1.63/1.83 tff(5476,plain,
% 1.63/1.83 (b(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[389, 5475, 342])).
% 1.63/1.83 tff(5477,plain,
% 1.63/1.83 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[313])).
% 1.63/1.83 tff(5478,plain,
% 1.63/1.83 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(symmetry,[status(thm)],[5477])).
% 1.63/1.83 tff(5479,plain,
% 1.63/1.83 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[313])).
% 1.63/1.83 tff(5480,plain,
% 1.63/1.83 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5479])).
% 1.63/1.83 tff(5481,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(symmetry,[status(thm)],[335])).
% 1.63/1.83 tff(5482,plain,
% 1.63/1.83 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[529, 316])).
% 1.63/1.83 tff(5483,plain,
% 1.63/1.83 (r(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5482, 315])).
% 1.63/1.83 tff(5484,plain,
% 1.63/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), 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(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5485,plain,
% 1.63/1.83 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5486,plain,
% 1.63/1.83 (((~![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(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5485])).
% 1.63/1.83 tff(5487,plain,
% 1.63/1.83 (((~![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(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.83 inference(transitivity,[status(thm)],[5486, 5484])).
% 1.63/1.83 tff(5488,plain,
% 1.63/1.83 ((~![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)))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5489,plain,
% 1.63/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5488, 5487])).
% 1.63/1.83 tff(5490,plain,
% 1.63/1.83 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5489, 141, 572])).
% 1.63/1.83 tff(5491,plain,
% 1.63/1.83 (~r(s(elem!1), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5490, 5483])).
% 1.63/1.83 tff(5492,plain,
% 1.63/1.83 (b(s(elem!1), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[484, 32, 481, 5491])).
% 1.63/1.83 tff(5493,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[537, 529, 310])).
% 1.63/1.83 tff(5494,plain,
% 1.63/1.83 (~r(s(s(elem!1)), z)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5493, 527])).
% 1.63/1.83 tff(5495,plain,
% 1.63/1.83 (b(s(s(elem!1)), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[542, 32, 258, 5494])).
% 1.63/1.83 tff(5496,plain,
% 1.63/1.83 (((~b(s(elem!1), z)) | (~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(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5497,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(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(X0, 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), s(s(elem!1))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5496])).
% 1.63/1.83 tff(5498,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(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(X0, 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), s(s(elem!1)))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[5497, 4981])).
% 1.63/1.83 tff(5499,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5500,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5499, 5498])).
% 1.63/1.83 tff(5501,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5500, 245, 288, 838, 5495, 5492])).
% 1.63/1.83 tff(5502,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5503,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5502, 397, 199, 310, 572, 838, 288])).
% 1.63/1.83 tff(5504,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[501, 5503, 332])).
% 1.63/1.83 tff(5505,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[1597, 333])).
% 1.63/1.83 tff(5506,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3905, 5505])).
% 1.63/1.83 tff(5507,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(5508,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5507, 5504, 199])).
% 1.63/1.83 tff(5509,plain,
% 1.63/1.83 (b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5508, 5481])).
% 1.63/1.83 tff(5510,plain,
% 1.63/1.83 (b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[2718, 5481])).
% 1.63/1.83 tff(5511,plain,
% 1.63/1.83 (~r(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[384, 141, 131, 220])).
% 1.63/1.83 tff(5512,plain,
% 1.63/1.83 (b(s(z), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[389, 5511, 342])).
% 1.63/1.83 tff(5513,plain,
% 1.63/1.83 (b(elem!1, s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[281, 2100, 210])).
% 1.63/1.83 tff(5514,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5515,plain,
% 1.63/1.83 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5516,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5515])).
% 1.63/1.83 tff(5517,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[5516, 5514])).
% 1.63/1.83 tff(5518,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5519,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5518, 5517])).
% 1.63/1.83 tff(5520,plain,
% 1.63/1.83 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5519, 245, 5513, 5512])).
% 1.63/1.83 tff(5521,plain,
% 1.63/1.83 (~b(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5520, 5510])).
% 1.63/1.83 tff(5522,plain,
% 1.63/1.83 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5521, 5480])).
% 1.63/1.83 tff(5523,plain,
% 1.63/1.83 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1820, 5522])).
% 1.63/1.83 tff(5524,plain,
% 1.63/1.83 (r(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5523, 5478])).
% 1.63/1.83 tff(5525,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5526,plain,
% 1.63/1.83 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5527,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5526])).
% 1.63/1.83 tff(5528,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[5527, 5525])).
% 1.63/1.83 tff(5529,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5530,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5529, 5528])).
% 1.63/1.83 tff(5531,plain,
% 1.63/1.83 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5530, 245, 5513, 1427, 5512])).
% 1.63/1.83 tff(5532,plain,
% 1.63/1.83 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5531, 5510])).
% 1.63/1.83 tff(5533,plain,
% 1.63/1.83 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[523, 32, 5017, 5532])).
% 1.63/1.83 tff(5534,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5535,plain,
% 1.63/1.83 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(5536,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[5535])).
% 1.63/1.83 tff(5537,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[5536, 5534])).
% 1.63/1.83 tff(5538,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(5539,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[5538, 5537])).
% 1.63/1.83 tff(5540,plain,
% 1.63/1.83 (~b(s(z), s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5539, 245, 5513, 1427, 5512])).
% 1.63/1.83 tff(5541,plain,
% 1.63/1.83 (r(s(z), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1133, 5540])).
% 1.63/1.84 tff(5542,plain,
% 1.63/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5543,plain,
% 1.63/1.84 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5544,plain,
% 1.63/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(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(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5543])).
% 1.63/1.84 tff(5545,plain,
% 1.63/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(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(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5544, 5542])).
% 1.63/1.84 tff(5546,plain,
% 1.63/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(5547,plain,
% 1.63/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5546, 5545])).
% 1.63/1.84 tff(5548,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5547, 141, 5541, 5533])).
% 1.63/1.84 tff(5549,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5548, 5524])).
% 1.63/1.84 tff(5550,plain,((~r(s(z), z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(5551,plain,
% 1.63/1.84 (~r(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5550, 5508, 1427, 199, 131, 520])).
% 1.63/1.84 tff(5552,plain,
% 1.63/1.84 (b(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[232, 5551])).
% 1.63/1.84 tff(5553,plain,
% 1.63/1.84 (~b(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[993, 245, 5552, 288, 838])).
% 1.63/1.84 tff(5554,plain,
% 1.63/1.84 (r(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[369, 5553, 348])).
% 1.63/1.84 tff(5555,plain,
% 1.63/1.84 (~r(elem!1, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4206, 5554, 572])).
% 1.63/1.84 tff(5556,plain,
% 1.63/1.84 (b(elem!1, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[281, 5555, 210])).
% 1.63/1.84 tff(5557,plain,
% 1.63/1.84 (~b(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5519, 245, 5556, 447, 5509])).
% 1.63/1.84 tff(5558,plain,
% 1.63/1.84 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5557, 5480])).
% 1.63/1.84 tff(5559,plain,
% 1.63/1.84 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1820, 5558])).
% 1.63/1.84 tff(5560,plain,
% 1.63/1.84 (r(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5559, 5478])).
% 1.63/1.84 tff(5561,plain,
% 1.63/1.84 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5530, 245, 5556, 1427, 447, 5509])).
% 1.63/1.84 tff(5562,plain,
% 1.63/1.84 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[523, 32, 520, 5561])).
% 1.63/1.84 tff(5563,plain,
% 1.63/1.84 (r(z, elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[310, 302])).
% 1.63/1.84 tff(5564,plain,
% 1.63/1.84 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[199])).
% 1.63/1.84 tff(5565,plain,
% 1.63/1.84 (r(s(elem!1), elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1366, 5564])).
% 1.63/1.84 tff(5566,plain,
% 1.63/1.84 (~r(z, s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3580, 141, 310, 1366])).
% 1.63/1.84 tff(5567,plain,
% 1.63/1.84 (b(z, s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[644, 5566])).
% 1.63/1.84 tff(5568,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.63/1.84 tff(5569,plain,
% 1.63/1.84 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[353, 11, 5568])).
% 1.63/1.84 tff(5570,plain,
% 1.63/1.84 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5502, 397, 5567, 288, 5565, 199, 310])).
% 1.63/1.84 tff(5571,plain,
% 1.63/1.84 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[501, 5570, 332])).
% 1.63/1.84 tff(5572,plain,
% 1.63/1.84 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5507, 5571, 199])).
% 1.63/1.84 tff(5573,plain,
% 1.63/1.84 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[199])).
% 1.63/1.84 tff(5574,plain,
% 1.63/1.84 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2377, 5569, 1366])).
% 1.63/1.84 tff(5575,plain,
% 1.63/1.84 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1239, 5574, 1309])).
% 1.63/1.84 tff(5576,plain,
% 1.63/1.84 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5575, 5573])).
% 1.63/1.84 tff(5577,plain,
% 1.63/1.84 (~r(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5550, 520, 199, 5576, 5572, 131])).
% 1.63/1.84 tff(5578,plain,
% 1.63/1.84 (b(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[232, 5577])).
% 1.63/1.84 tff(5579,plain,
% 1.63/1.84 (~b(s(s(s(elem!1))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3353, 5578, 5569, 288, 5567, 9, 5565, 5563])).
% 1.63/1.84 tff(5580,plain,
% 1.63/1.84 (r(s(s(s(elem!1))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[37, 5579])).
% 1.63/1.84 tff(5581,plain,
% 1.63/1.84 (~r(elem!1, s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4128, 5580, 131])).
% 1.63/1.84 tff(5582,plain,
% 1.63/1.84 (b(elem!1, s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1724, 5581, 1717])).
% 1.63/1.84 tff(5583,plain,
% 1.63/1.84 (~b(s(z), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[663, 5578, 5565, 5563])).
% 1.63/1.84 tff(5584,plain,
% 1.63/1.84 (r(s(z), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[440, 5583, 9])).
% 1.63/1.84 tff(5585,plain,
% 1.63/1.84 (~r(s(s(s(elem!1))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3350, 141, 5569, 5584])).
% 1.63/1.84 tff(5586,plain,
% 1.63/1.84 (b(s(s(s(elem!1))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[265, 5585])).
% 1.63/1.84 tff(5587,plain,
% 1.63/1.84 (~r(s(z), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2411, 141, 5569, 5584])).
% 1.63/1.84 tff(5588,plain,
% 1.63/1.84 (b(s(z), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1133, 5587])).
% 1.63/1.84 tff(5589,plain,
% 1.63/1.84 (~b(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[993, 245, 5578, 288, 5567])).
% 1.63/1.84 tff(5590,plain,
% 1.63/1.84 (r(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[369, 5589, 348])).
% 1.63/1.84 tff(5591,plain,
% 1.63/1.84 (~r(elem!1, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4206, 5590, 5565])).
% 1.63/1.84 tff(5592,plain,
% 1.63/1.84 (b(elem!1, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[281, 5591, 210])).
% 1.63/1.84 tff(5593,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5594,plain,
% 1.63/1.84 (((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5595,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5594])).
% 1.63/1.84 tff(5596,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5595, 5593])).
% 1.63/1.84 tff(5597,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(5598,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5597, 5596])).
% 1.63/1.84 tff(5599,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5598, 245, 5592, 5588, 5586, 5582])).
% 1.63/1.84 tff(5600,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), z)) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(5601,plain,
% 1.63/1.84 (b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5600, 11, 131, 1717, 9, 1366, 310, 1309, 199, 288])).
% 1.63/1.84 tff(5602,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5603,plain,
% 1.63/1.84 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5604,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5603])).
% 1.63/1.84 tff(5605,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5604, 5602])).
% 1.63/1.84 tff(5606,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(5607,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5606, 5605])).
% 1.63/1.84 tff(5608,plain,
% 1.63/1.84 (~b(s(s(s(elem!1))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5607, 245, 5601, 5556, 1427, 5552, 838])).
% 1.63/1.84 tff(5609,plain,
% 1.63/1.84 (r(s(s(s(elem!1))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[265, 5608])).
% 1.63/1.84 tff(5610,plain,
% 1.63/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5611,plain,
% 1.63/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(5612,plain,
% 1.63/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5611, 5610])).
% 1.63/1.84 tff(5613,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5612, 141, 5609, 5562])).
% 1.63/1.84 tff(5614,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5613, 5560])).
% 1.63/1.84 tff(5615,plain,((s(s(s(elem!1))) = s(elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (~r(z, s(s(s(s(elem!1)))))) | (elem!1 = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(5616,plain,
% 1.63/1.84 (s(s(s(elem!1))) = s(elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5615, 5476, 199, 1427, 5474, 1277, 5472, 131, 304, 1673, 9, 5470, 1304])).
% 1.63/1.84 tff(5617,plain,
% 1.63/1.84 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5616])).
% 1.63/1.84 tff(5618,plain,
% 1.63/1.84 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.84 inference(symmetry,[status(thm)],[5617])).
% 1.63/1.84 tff(5619,plain,
% 1.63/1.84 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5618])).
% 1.63/1.84 tff(5620,plain,
% 1.63/1.84 (~b(s(s(s(elem!1))), elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[564, 5619])).
% 1.63/1.84 tff(5621,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1427, 5620])).
% 1.63/1.84 tff(5622,plain,(b(s(elem!1), elem!1) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(5623,plain,
% 1.63/1.84 (b(s(elem!1), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5622, 152, 5467, 129, 9, 176, 1])).
% 1.63/1.84 tff(5624,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[199])).
% 1.63/1.84 tff(5625,plain,
% 1.63/1.84 (r(elem!1, s(elem!1))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[406, 5624])).
% 1.63/1.84 tff(5626,plain,
% 1.63/1.84 (~r(s(elem!1), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1082, 5625, 131])).
% 1.63/1.84 tff(5627,plain,
% 1.63/1.84 (b(s(elem!1), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1039, 5626])).
% 1.63/1.84 tff(5628,plain,
% 1.63/1.84 (~r(z, s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1350, 406, 106])).
% 1.63/1.84 tff(5629,plain,
% 1.63/1.84 (b(z, s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[644, 5628])).
% 1.63/1.84 tff(5630,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4612, 268, 402])).
% 1.63/1.84 tff(5631,plain,
% 1.63/1.84 (~r(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[225, 5630, 106])).
% 1.63/1.84 tff(5632,plain,
% 1.63/1.84 (b(s(z), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[232, 5631])).
% 1.63/1.84 tff(5633,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5634,plain,
% 1.63/1.84 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5635,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5634])).
% 1.63/1.84 tff(5636,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5635, 5633])).
% 1.63/1.84 tff(5637,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(5638,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5637, 5636])).
% 1.63/1.84 tff(5639,plain,
% 1.63/1.84 ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5638, 245, 308, 5632, 5629])).
% 1.63/1.84 tff(5640,plain,
% 1.63/1.84 (~b(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5639, 5627])).
% 1.63/1.84 tff(5641,plain,
% 1.63/1.84 (r(s(elem!1), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[369, 5640, 358])).
% 1.63/1.84 tff(5642,plain,
% 1.63/1.84 (((~![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(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5643,plain,
% 1.63/1.84 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5644,plain,
% 1.63/1.84 (((~![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(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5643])).
% 1.63/1.84 tff(5645,plain,
% 1.63/1.84 (((~![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(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5644, 5642])).
% 1.63/1.84 tff(5646,plain,
% 1.63/1.84 ((~![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))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(5647,plain,
% 1.63/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5646, 5645])).
% 1.63/1.84 tff(5648,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5647, 141, 5625, 268, 5641])).
% 1.63/1.84 tff(5649,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(5650,plain,
% 1.63/1.84 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5649, 268, 358, 308, 131, 199, 106])).
% 1.63/1.84 tff(5651,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[420, 5650, 164])).
% 1.63/1.84 tff(5652,plain,
% 1.63/1.84 (b(elem!1, s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[428, 5651, 402])).
% 1.63/1.84 tff(5653,plain,
% 1.63/1.84 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2334, 5652, 1427, 308])).
% 1.63/1.84 tff(5654,plain,
% 1.63/1.84 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2091, 32, 5653])).
% 1.63/1.84 tff(5655,plain,
% 1.63/1.84 (r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5654, 2081])).
% 1.63/1.84 tff(5656,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5657,plain,
% 1.63/1.84 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5658,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5657])).
% 1.63/1.84 tff(5659,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5658, 5656])).
% 1.63/1.84 tff(5660,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(5661,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[5660, 5659])).
% 1.63/1.84 tff(5662,plain,
% 1.63/1.84 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5661, 245, 308, 1427, 1103, 446])).
% 1.63/1.84 tff(5663,plain,
% 1.63/1.84 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[523, 32, 5017, 5662])).
% 1.63/1.84 tff(5664,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5665,plain,
% 1.63/1.84 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(5666,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5665])).
% 1.63/1.85 tff(5667,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5666, 5664])).
% 1.63/1.85 tff(5668,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5669,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5668, 5667])).
% 1.63/1.85 tff(5670,plain,
% 1.63/1.85 (~b(s(elem!1), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5669, 245, 308, 1103, 446])).
% 1.63/1.85 tff(5671,plain,
% 1.63/1.85 (r(s(elem!1), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[484, 32, 481, 5670])).
% 1.63/1.85 tff(5672,plain,
% 1.63/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(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(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5673,plain,
% 1.63/1.85 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5674,plain,
% 1.63/1.85 (((~![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(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5673])).
% 1.63/1.85 tff(5675,plain,
% 1.63/1.85 (((~![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(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5674, 5672])).
% 1.63/1.85 tff(5676,plain,
% 1.63/1.85 ((~![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)))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5677,plain,
% 1.63/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5676, 5675])).
% 1.63/1.85 tff(5678,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5677, 141, 2133, 5671, 5663])).
% 1.63/1.85 tff(5679,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(5680,plain,
% 1.63/1.85 (~b(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5679, 5655, 520, 397, 308, 1427, 5652])).
% 1.63/1.85 tff(5681,plain,
% 1.63/1.85 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5680, 337])).
% 1.63/1.85 tff(5682,plain,
% 1.63/1.85 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[501, 5681, 332])).
% 1.63/1.85 tff(5683,plain,
% 1.63/1.85 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5682, 316])).
% 1.63/1.85 tff(5684,plain,
% 1.63/1.85 (r(s(s(elem!1)), elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5683, 315])).
% 1.63/1.85 tff(5685,plain,
% 1.63/1.85 (((~![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)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5686,plain,
% 1.63/1.85 ((~![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)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5687,plain,
% 1.63/1.85 ((~![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))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5686, 5685])).
% 1.63/1.85 tff(5688,plain,
% 1.63/1.85 (~r(s(s(elem!1)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5687, 141, 289, 5684])).
% 1.63/1.85 tff(5689,plain,
% 1.63/1.85 (b(s(s(elem!1)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[542, 32, 258, 5688])).
% 1.63/1.85 tff(5690,plain,
% 1.63/1.85 (~r(z, s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[4226, 5630, 106])).
% 1.63/1.85 tff(5691,plain,
% 1.63/1.85 (b(z, s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1421, 5690])).
% 1.63/1.85 tff(5692,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5693,plain,
% 1.63/1.85 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5694,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5693])).
% 1.63/1.85 tff(5695,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5694, 5692])).
% 1.63/1.85 tff(5696,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5697,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5696, 5695])).
% 1.63/1.85 tff(5698,plain,
% 1.63/1.85 (~b(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5697, 245, 5632, 5691, 5689])).
% 1.63/1.85 tff(5699,plain,
% 1.63/1.85 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5698, 5480])).
% 1.63/1.85 tff(5700,plain,
% 1.63/1.85 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1820, 5699])).
% 1.63/1.85 tff(5701,plain,
% 1.63/1.85 (r(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5700, 5478])).
% 1.63/1.85 tff(5702,plain,
% 1.63/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5703,plain,
% 1.63/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5704,plain,
% 1.63/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5703, 5702])).
% 1.63/1.85 tff(5705,plain,
% 1.63/1.85 (~r(s(s(elem!1)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5704, 141, 268, 5684])).
% 1.63/1.85 tff(5706,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5705, 5701])).
% 1.63/1.85 tff(5707,plain,((~r(elem!1, s(z))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(5708,plain,
% 1.63/1.85 (~r(elem!1, s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5707, 11, 289, 308, 1427, 199, 164, 348, 131, 106])).
% 1.63/1.85 tff(5709,plain,
% 1.63/1.85 (b(elem!1, s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[281, 5708, 210])).
% 1.63/1.85 tff(5710,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5711,plain,
% 1.63/1.85 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5712,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5711])).
% 1.63/1.85 tff(5713,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5712, 5710])).
% 1.63/1.85 tff(5714,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5715,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5714, 5713])).
% 1.63/1.85 tff(5716,plain,
% 1.63/1.85 (~b(s(s(s(elem!1))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5715, 245, 301, 1427, 447])).
% 1.63/1.85 tff(5717,plain,
% 1.63/1.85 (r(s(s(s(elem!1))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[265, 5716])).
% 1.63/1.85 tff(5718,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5719,plain,
% 1.63/1.85 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5720,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5719])).
% 1.63/1.85 tff(5721,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5720, 5718])).
% 1.63/1.85 tff(5722,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5723,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5722, 5721])).
% 1.63/1.85 tff(5724,plain,
% 1.63/1.85 (~b(s(elem!1), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5723, 245, 301, 308, 447])).
% 1.63/1.85 tff(5725,plain,
% 1.63/1.85 (r(s(elem!1), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[369, 5724, 358])).
% 1.63/1.85 tff(5726,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5727,plain,
% 1.63/1.85 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~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(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5728,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5727])).
% 1.63/1.85 tff(5729,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5728, 5726])).
% 1.63/1.85 tff(5730,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5731,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5730, 5729])).
% 1.63/1.85 tff(5732,plain,
% 1.63/1.85 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5731, 245, 301, 308, 1427, 447])).
% 1.63/1.85 tff(5733,plain,
% 1.63/1.85 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[353, 5732, 11])).
% 1.63/1.85 tff(5734,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[377, 141, 5733, 5725, 5717])).
% 1.63/1.85 tff(5735,plain,((~b(s(z), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(5736,plain,
% 1.63/1.85 (~b(s(z), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5735, 11, 348, 5709, 308, 1427])).
% 1.63/1.85 tff(5737,plain,
% 1.63/1.85 (r(s(z), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[389, 5736, 342])).
% 1.63/1.85 tff(5738,plain,
% 1.63/1.85 (~r(s(z), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[668, 141, 289, 5737])).
% 1.63/1.85 tff(5739,plain,
% 1.63/1.85 (b(s(z), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[232, 5738])).
% 1.63/1.85 tff(5740,plain,
% 1.63/1.85 (~b(s(z), s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[661, 245, 355, 5627, 5629])).
% 1.63/1.85 tff(5741,plain,
% 1.63/1.85 (r(s(z), s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[440, 5740, 9])).
% 1.63/1.85 tff(5742,plain,
% 1.63/1.85 (((~![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), s(elem!1))) | (~r(s(z), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5743,plain,
% 1.63/1.85 ((~![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)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5744,plain,
% 1.63/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5743, 5742])).
% 1.63/1.85 tff(5745,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5744, 141, 5625, 5741, 619])).
% 1.63/1.85 tff(5746,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), elem!1)) | (s(z) = s(elem!1)) | (~b(s(z), z)) | (~r(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(5747,plain,
% 1.63/1.85 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5746, 5737, 9, 5739, 131, 199, 106])).
% 1.63/1.85 tff(5748,plain,
% 1.63/1.85 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[420, 5747, 164])).
% 1.63/1.85 tff(5749,plain,
% 1.63/1.85 (b(elem!1, s(elem!1))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[428, 5748, 402])).
% 1.63/1.85 tff(5750,plain,
% 1.63/1.85 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(5751,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(elem!1, s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5750])).
% 1.63/1.85 tff(5752,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5751, 2469])).
% 1.63/1.85 tff(5753,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(5754,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[5753, 5752])).
% 1.63/1.86 tff(5755,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5754, 245, 301, 308, 1103, 655])).
% 1.63/1.86 tff(5756,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(5757,plain,
% 1.63/1.86 (~b(s(z), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5756, 5709, 308, 5749])).
% 1.63/1.86 tff(5758,plain,
% 1.63/1.86 (r(s(z), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[440, 5757, 9])).
% 1.63/1.86 tff(5759,plain,
% 1.63/1.86 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[5573])).
% 1.63/1.86 tff(5760,plain,
% 1.63/1.86 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[1427, 5759])).
% 1.63/1.86 tff(5761,plain,
% 1.63/1.86 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1295, 5748, 5760, 309])).
% 1.63/1.86 tff(5762,plain,
% 1.63/1.86 (r(s(s(s(elem!1))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[353, 5761, 11])).
% 1.63/1.86 tff(5763,plain,
% 1.63/1.86 (~r(s(s(s(elem!1))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3350, 141, 5762, 5758])).
% 1.63/1.86 tff(5764,plain,
% 1.63/1.86 (b(s(s(s(elem!1))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[265, 5763])).
% 1.63/1.86 tff(5765,plain,
% 1.63/1.86 (~r(s(z), s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[2411, 141, 5762, 5758])).
% 1.63/1.86 tff(5766,plain,
% 1.63/1.86 (b(s(z), s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1133, 5765])).
% 1.63/1.86 tff(5767,plain,
% 1.63/1.86 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5768,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5767])).
% 1.63/1.86 tff(5769,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[5768, 4700])).
% 1.63/1.86 tff(5770,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(5771,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5770, 5769])).
% 1.63/1.86 tff(5772,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5771, 245, 5709, 1427, 5766, 5764])).
% 1.63/1.86 tff(5773,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(z) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(5774,plain,
% 1.63/1.86 (s(s(s(elem!1))) = s(elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5773, 9, 5467, 5623, 7, 129, 152, 106, 176])).
% 1.63/1.86 tff(5775,plain,
% 1.63/1.86 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 1.63/1.86 inference(transitivity,[status(thm)],[160, 5774])).
% 1.63/1.86 tff(5776,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5775])).
% 1.63/1.86 tff(5777,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[5776])).
% 1.63/1.86 tff(5778,plain,
% 1.63/1.86 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5777])).
% 1.63/1.86 tff(5779,plain,
% 1.63/1.86 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 1.63/1.86 inference(transitivity,[status(thm)],[598, 553])).
% 1.63/1.86 tff(5780,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5779])).
% 1.63/1.86 tff(5781,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[5780])).
% 1.63/1.86 tff(5782,plain,
% 1.63/1.86 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5781])).
% 1.63/1.86 tff(5783,plain,
% 1.63/1.86 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1051, 199])).
% 1.63/1.86 tff(5784,plain,
% 1.63/1.86 (~(s(elem!1) = s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[594, 553, 199, 9])).
% 1.63/1.86 tff(5785,plain,
% 1.63/1.86 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[612, 553, 199, 5784])).
% 1.63/1.86 tff(5786,plain,
% 1.63/1.86 (~r(s(s(s(s(s(z))))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[731, 723, 131])).
% 1.63/1.86 tff(5787,plain,
% 1.63/1.86 (b(s(s(s(s(s(z))))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[738, 5786])).
% 1.63/1.86 tff(5788,plain,
% 1.63/1.86 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[748, 723, 289])).
% 1.63/1.86 tff(5789,plain,
% 1.63/1.86 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[758, 5788])).
% 1.63/1.86 tff(5790,plain,
% 1.63/1.86 (~r(s(elem!1), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1082, 1367, 131])).
% 1.63/1.86 tff(5791,plain,
% 1.63/1.86 (b(s(elem!1), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1039, 5790])).
% 1.63/1.86 tff(5792,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5793,plain,
% 1.63/1.86 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5794,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5793])).
% 1.63/1.86 tff(5795,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[5794, 5792])).
% 1.63/1.86 tff(5796,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(5797,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5796, 5795])).
% 1.63/1.86 tff(5798,plain,
% 1.63/1.86 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5797, 245, 5791, 5789, 5787])).
% 1.63/1.86 tff(5799,plain,
% 1.63/1.86 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5798, 676])).
% 1.63/1.86 tff(5800,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[797, 5799, 673])).
% 1.63/1.86 tff(5801,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5800, 5780])).
% 1.63/1.86 tff(5802,plain,
% 1.63/1.86 (((~![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(s(s(z))))))) | (~r(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(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5803,plain,
% 1.63/1.86 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5804,plain,
% 1.63/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5803])).
% 1.63/1.86 tff(5805,plain,
% 1.63/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[5804, 5802])).
% 1.63/1.86 tff(5806,plain,
% 1.63/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(5807,plain,
% 1.63/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5806, 5805])).
% 1.63/1.86 tff(5808,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5807, 141, 1367, 723, 5801])).
% 1.63/1.86 tff(5809,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(5810,plain,
% 1.63/1.86 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5809, 5625, 553, 199, 5785, 131, 289])).
% 1.63/1.86 tff(5811,plain,
% 1.63/1.86 (b(elem!1, s(s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[720, 5810, 5783])).
% 1.63/1.86 tff(5812,plain,
% 1.63/1.86 (~r(elem!1, s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5649, 406, 348, 308, 131, 199, 106])).
% 1.63/1.86 tff(5813,plain,
% 1.63/1.86 (b(elem!1, s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[281, 5812, 210])).
% 1.63/1.86 tff(5814,plain,
% 1.63/1.86 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[775, 5783])).
% 1.63/1.86 tff(5815,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5816,plain,
% 1.63/1.86 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5817,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5816])).
% 1.63/1.86 tff(5818,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.86 inference(transitivity,[status(thm)],[5817, 5815])).
% 1.63/1.86 tff(5819,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(5820,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5819, 5818])).
% 1.63/1.86 tff(5821,plain,
% 1.63/1.86 (~b(s(z), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5820, 245, 301, 308, 5512])).
% 1.63/1.86 tff(5822,plain,
% 1.63/1.86 (r(s(z), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[440, 5821, 9])).
% 1.63/1.86 tff(5823,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.63/1.86 tff(5824,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[928, 5780])).
% 1.63/1.86 tff(5825,plain,
% 1.63/1.86 (((~![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(z))))), elem!1)) | (~r(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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5826,plain,
% 1.63/1.86 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5827,plain,
% 1.63/1.86 (((~![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(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5826])).
% 1.63/1.86 tff(5828,plain,
% 1.63/1.86 (((~![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(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[5827, 5825])).
% 1.63/1.86 tff(5829,plain,
% 1.63/1.86 ((~![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(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(5830,plain,
% 1.63/1.86 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5829, 5828])).
% 1.63/1.86 tff(5831,plain,
% 1.63/1.86 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5830, 141, 1367, 5824])).
% 1.63/1.86 tff(5832,plain,
% 1.63/1.86 (b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[787, 5831, 5814])).
% 1.63/1.86 tff(5833,plain,
% 1.63/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5834,plain,
% 1.63/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(5835,plain,
% 1.63/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5834, 5833])).
% 1.63/1.86 tff(5836,plain,
% 1.63/1.86 (~r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5835, 141, 486, 5824])).
% 1.63/1.86 tff(5837,plain,
% 1.63/1.86 (b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[809, 5836])).
% 1.63/1.86 tff(5838,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5839,plain,
% 1.63/1.86 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5840,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[5839])).
% 1.63/1.86 tff(5841,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.86 inference(transitivity,[status(thm)],[5840, 5838])).
% 1.63/1.86 tff(5842,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(5843,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[5842, 5841])).
% 1.63/1.86 tff(5844,plain,
% 1.63/1.86 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5843, 245, 447, 5823, 919])).
% 1.63/1.86 tff(5845,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5844, 5837, 5832])).
% 1.63/1.86 tff(5846,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(5847,plain,
% 1.63/1.86 (~b(s(s(s(s(s(z))))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5846, 5512, 5823, 5822, 1367, 553, 199, 5785, 5791, 838])).
% 1.63/1.86 tff(5848,plain,
% 1.63/1.86 (r(s(s(s(s(s(z))))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[738, 5847])).
% 1.63/1.86 tff(5849,plain,
% 1.63/1.86 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1161, 141, 131, 5848])).
% 1.63/1.86 tff(5850,plain,
% 1.63/1.86 (b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[787, 5849, 5814])).
% 1.63/1.86 tff(5851,plain,
% 1.63/1.86 (((~![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(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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5852,plain,
% 1.63/1.86 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(5853,plain,
% 1.63/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5852])).
% 1.63/1.87 tff(5854,plain,
% 1.63/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[5853, 5851])).
% 1.63/1.87 tff(5855,plain,
% 1.63/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5856,plain,
% 1.63/1.87 ((~![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(z), s(s(s(s(s(z)))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5855, 5854])).
% 1.63/1.87 tff(5857,plain,
% 1.63/1.87 (~r(s(z), s(s(s(s(s(z))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5856, 141, 220, 5848])).
% 1.63/1.87 tff(5858,plain,
% 1.63/1.87 (b(s(z), s(s(s(s(s(z))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1698, 5857])).
% 1.63/1.87 tff(5859,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5860,plain,
% 1.63/1.87 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5861,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5860])).
% 1.63/1.87 tff(5862,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.87 inference(transitivity,[status(thm)],[5861, 5859])).
% 1.63/1.87 tff(5863,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5864,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5863, 5862])).
% 1.63/1.87 tff(5865,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5864, 245, 301, 5512, 5858, 5850])).
% 1.63/1.87 tff(5866,plain,((~r(s(z), z)) | (~b(elem!1, s(z))) | (~r(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(z, s(elem!1))) | (s(z) = s(elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(5867,plain,
% 1.63/1.87 (~r(s(z), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5866, 5813, 131, 5811, 5625, 553, 199, 5629, 9, 308])).
% 1.63/1.87 tff(5868,plain,
% 1.63/1.87 (b(s(z), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[232, 5867])).
% 1.63/1.87 tff(5869,plain,
% 1.63/1.87 (~b(s(elem!1), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5638, 245, 308, 5868, 5627, 5629])).
% 1.63/1.87 tff(5870,plain,
% 1.63/1.87 (r(s(elem!1), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[369, 5869, 348])).
% 1.63/1.87 tff(5871,plain,
% 1.63/1.87 (~r(s(z), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5746, 5868, 9, 406, 131, 199, 106])).
% 1.63/1.87 tff(5872,plain,
% 1.63/1.87 (b(s(z), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[389, 5871, 342])).
% 1.63/1.87 tff(5873,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5874,plain,
% 1.63/1.87 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5875,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5874])).
% 1.63/1.87 tff(5876,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.63/1.87 inference(transitivity,[status(thm)],[5875, 5873])).
% 1.63/1.87 tff(5877,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5878,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5877, 5876])).
% 1.63/1.87 tff(5879,plain,
% 1.63/1.87 (~b(s(z), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5878, 245, 5813, 308, 5868, 5872])).
% 1.63/1.87 tff(5880,plain,
% 1.63/1.87 (r(s(z), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[440, 5879, 9])).
% 1.63/1.87 tff(5881,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5846, 5880, 5811, 5872, 5625, 553, 199, 5785, 5627, 5629])).
% 1.63/1.87 tff(5882,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[738, 5881])).
% 1.63/1.87 tff(5883,plain,
% 1.63/1.87 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1161, 141, 131, 5882])).
% 1.63/1.87 tff(5884,plain,
% 1.63/1.87 (b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[787, 5883, 5814])).
% 1.63/1.87 tff(5885,plain,
% 1.63/1.87 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5886,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5885])).
% 1.63/1.87 tff(5887,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.87 inference(transitivity,[status(thm)],[5886, 777])).
% 1.63/1.87 tff(5888,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5889,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5888, 5887])).
% 1.63/1.87 tff(5890,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5889, 245, 5813, 5872, 5884])).
% 1.63/1.87 tff(5891,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[809, 5890])).
% 1.63/1.87 tff(5892,plain,
% 1.63/1.87 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1003, 5891, 5870])).
% 1.63/1.87 tff(5893,plain,
% 1.63/1.87 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5892, 5782])).
% 1.63/1.87 tff(5894,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5895,plain,
% 1.63/1.87 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5896,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5895])).
% 1.63/1.87 tff(5897,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[5896, 5894])).
% 1.63/1.87 tff(5898,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5899,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5898, 5897])).
% 1.63/1.87 tff(5900,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5899, 245, 5813, 308, 5872, 5884])).
% 1.63/1.87 tff(5901,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5900, 676])).
% 1.63/1.87 tff(5902,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[797, 5901, 5785])).
% 1.63/1.87 tff(5903,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5902, 5893])).
% 1.63/1.87 tff(5904,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(5905,plain,
% 1.63/1.87 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5904, 5774, 152, 5623, 129, 9, 106, 176])).
% 1.63/1.87 tff(5906,plain,
% 1.63/1.87 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[420, 5905, 7])).
% 1.63/1.87 tff(5907,plain,
% 1.63/1.87 (elem!1 = s(s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[401, 152])).
% 1.63/1.87 tff(5908,plain,
% 1.63/1.87 (b(elem!1, s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[428, 5906, 5907])).
% 1.63/1.87 tff(5909,plain,
% 1.63/1.87 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[1067])).
% 1.63/1.87 tff(5910,plain,
% 1.63/1.87 (~(elem!1 = s(z))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[209, 5909])).
% 1.63/1.87 tff(5911,plain,
% 1.63/1.87 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[674])).
% 1.63/1.87 tff(5912,plain,
% 1.63/1.87 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.63/1.87 inference(symmetry,[status(thm)],[5911])).
% 1.63/1.87 tff(5913,plain,
% 1.63/1.87 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(commutativity,[status(thm)],[])).
% 1.63/1.87 tff(5914,plain,
% 1.63/1.87 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 1.63/1.87 inference(symmetry,[status(thm)],[5913])).
% 1.63/1.87 tff(5915,plain,
% 1.63/1.87 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5914])).
% 1.63/1.87 tff(5916,plain,
% 1.63/1.87 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5785, 5915])).
% 1.63/1.87 tff(5917,plain,
% 1.63/1.87 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[674])).
% 1.63/1.87 tff(5918,plain,
% 1.63/1.87 ((~r(s(elem!1), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5917])).
% 1.63/1.87 tff(5919,plain,
% 1.63/1.87 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1065, 199, 9])).
% 1.63/1.87 tff(5920,assumption,(s(s(s(s(s(z))))) = s(elem!1)), introduced(assumption)).
% 1.63/1.87 tff(5921,plain,
% 1.63/1.87 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.63/1.87 inference(symmetry,[status(thm)],[5920])).
% 1.63/1.87 tff(5922,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1153, 5921])).
% 1.63/1.87 tff(5923,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (s(elem!1) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(5924,plain,
% 1.63/1.87 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5923, 5919])).
% 1.63/1.87 tff(5925,plain,
% 1.63/1.87 (b(elem!1, s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[428, 10, 402])).
% 1.63/1.87 tff(5926,assumption,(~(s(s(s(s(s(z))))) = s(elem!1))), introduced(assumption)).
% 1.63/1.87 tff(5927,plain,
% 1.63/1.87 (((~![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(s(z))))), z)) | (~r(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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5928,plain,
% 1.63/1.87 ((~![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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5929,plain,
% 1.63/1.87 ((~![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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5928, 5927])).
% 1.63/1.87 tff(5930,plain,
% 1.63/1.87 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5929, 141, 1097, 722])).
% 1.63/1.87 tff(5931,plain,
% 1.63/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5932,plain,
% 1.63/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5933,plain,
% 1.63/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5932, 5931])).
% 1.63/1.87 tff(5934,plain,
% 1.63/1.87 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5933, 32, 5930, 5926])).
% 1.63/1.87 tff(5935,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5936,plain,
% 1.63/1.87 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5937,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5936])).
% 1.63/1.87 tff(5938,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[5937, 5935])).
% 1.63/1.87 tff(5939,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5940,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5939, 5938])).
% 1.63/1.87 tff(5941,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5940, 245, 308, 1103, 1163, 5934])).
% 1.63/1.87 tff(5942,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(s(z))))) = s(elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(elem!1), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(5943,plain,
% 1.63/1.87 (~r(s(s(s(s(s(z))))), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5942, 1097, 5925, 5924, 5814, 308, 131])).
% 1.63/1.87 tff(5944,plain,
% 1.63/1.87 (b(s(s(s(s(s(z))))), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[738, 5943])).
% 1.63/1.87 tff(5945,plain,
% 1.63/1.87 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.63/1.87 inference(monotonicity,[status(thm)],[553])).
% 1.63/1.87 tff(5946,plain,
% 1.63/1.87 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 1.63/1.87 inference(symmetry,[status(thm)],[5945])).
% 1.63/1.87 tff(5947,plain,
% 1.63/1.87 (r(s(s(s(elem!1))), z)),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[1097, 5946])).
% 1.63/1.87 tff(5948,plain,
% 1.63/1.87 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[553])).
% 1.63/1.87 tff(5949,plain,
% 1.63/1.87 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.63/1.87 inference(symmetry,[status(thm)],[5948])).
% 1.63/1.87 tff(5950,plain,
% 1.63/1.87 (~r(s(z), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1111, 1097, 106, 10, 9, 308, 5925])).
% 1.63/1.87 tff(5951,plain,
% 1.63/1.87 (b(s(z), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[232, 5950])).
% 1.63/1.87 tff(5952,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5953,plain,
% 1.63/1.87 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~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))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5954,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[5953])).
% 1.63/1.87 tff(5955,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[5954, 5952])).
% 1.63/1.87 tff(5956,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5957,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5956, 5955])).
% 1.63/1.87 tff(5958,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5957, 245, 355, 5691, 919])).
% 1.63/1.87 tff(5959,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[809, 5958])).
% 1.63/1.87 tff(5960,plain,
% 1.63/1.87 (((~![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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(5961,plain,
% 1.63/1.87 ((~![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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(5962,plain,
% 1.63/1.87 ((~![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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5961, 5960])).
% 1.63/1.87 tff(5963,plain,
% 1.63/1.87 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5962, 141, 268, 5959])).
% 1.63/1.87 tff(5964,plain,
% 1.63/1.87 (b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[787, 5963, 5814])).
% 1.63/1.87 tff(5965,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5940, 245, 308, 1103, 5964])).
% 1.63/1.87 tff(5966,plain,
% 1.63/1.87 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[5965, 676])).
% 1.63/1.87 tff(5967,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[797, 5966, 917])).
% 1.63/1.87 tff(5968,plain,
% 1.63/1.87 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[5967, 5780])).
% 1.63/1.88 tff(5969,plain,
% 1.63/1.88 (~r(s(elem!1), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1003, 5968, 5959])).
% 1.63/1.88 tff(5970,plain,
% 1.63/1.88 (b(s(elem!1), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[369, 5969, 358])).
% 1.63/1.88 tff(5971,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(5972,plain,
% 1.63/1.88 (((~b(z, s(z))) | (~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))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(5973,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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(X0, 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)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[5972])).
% 1.63/1.88 tff(5974,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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(X0, 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))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[5973, 5971])).
% 1.63/1.88 tff(5975,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(5976,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[5975, 5974])).
% 1.63/1.88 tff(5977,plain,
% 1.63/1.88 (~b(z, s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5976, 245, 355, 5970, 5691])).
% 1.63/1.88 tff(5978,plain,
% 1.63/1.88 (r(z, s(elem!1))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[644, 5977])).
% 1.63/1.88 tff(5979,plain,
% 1.63/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(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(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(5980,plain,
% 1.63/1.88 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(5981,plain,
% 1.63/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[5980])).
% 1.63/1.88 tff(5982,plain,
% 1.63/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[5981, 5979])).
% 1.63/1.88 tff(5983,plain,
% 1.63/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(5984,plain,
% 1.63/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[5983, 5982])).
% 1.63/1.88 tff(5985,plain,
% 1.63/1.88 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5984, 141, 5978, 5968])).
% 1.63/1.88 tff(5986,plain,
% 1.63/1.88 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[758, 5985])).
% 1.63/1.88 tff(5987,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(5988,plain,
% 1.63/1.88 (((~b(s(z), z)) | (~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(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(5989,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[5988])).
% 1.63/1.88 tff(5990,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[5989, 5987])).
% 1.63/1.88 tff(5991,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(5992,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[5991, 5990])).
% 1.63/1.88 tff(5993,plain,
% 1.63/1.88 (~b(s(z), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[5992, 245, 355, 5691, 919])).
% 1.63/1.88 tff(5994,plain,
% 1.63/1.88 (r(s(z), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1698, 5993])).
% 1.63/1.88 tff(5995,plain,
% 1.63/1.88 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(symmetry,[status(thm)],[5917])).
% 1.63/1.88 tff(5996,plain,
% 1.63/1.88 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[917, 5915])).
% 1.63/1.88 tff(5997,plain,
% 1.63/1.88 ((~b(s(elem!1), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[5911])).
% 1.63/1.88 tff(5998,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(5999,plain,
% 1.63/1.88 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6000,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[5999])).
% 1.63/1.88 tff(6001,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.63/1.88 inference(transitivity,[status(thm)],[6000, 5998])).
% 1.63/1.88 tff(6002,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(6003,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6002, 6001])).
% 1.63/1.88 tff(6004,plain,
% 1.63/1.88 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6003, 245, 308, 1103, 5964])).
% 1.63/1.88 tff(6005,plain,
% 1.63/1.88 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6004, 5997])).
% 1.63/1.88 tff(6006,plain,
% 1.63/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6007,plain,
% 1.63/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(6008,plain,
% 1.63/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6007, 6006])).
% 1.63/1.88 tff(6009,plain,
% 1.63/1.88 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6008, 32])).
% 1.63/1.88 tff(6010,plain,
% 1.63/1.88 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6009, 6005, 5996])).
% 1.63/1.88 tff(6011,plain,
% 1.63/1.88 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6010, 5995])).
% 1.63/1.88 tff(6012,assumption,(r(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.63/1.88 tff(6013,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.63/1.88 tff(6014,plain,
% 1.63/1.88 (((~![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(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6015,plain,
% 1.63/1.88 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6016,plain,
% 1.63/1.88 (((~![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(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[6015])).
% 1.63/1.88 tff(6017,plain,
% 1.63/1.88 (((~![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(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[6016, 6014])).
% 1.63/1.88 tff(6018,plain,
% 1.63/1.88 ((~![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(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(6019,plain,
% 1.63/1.88 ((~![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(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6018, 6017])).
% 1.63/1.88 tff(6020,plain,
% 1.63/1.88 (~r(s(elem!1), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6019, 141, 6013, 6012])).
% 1.63/1.88 tff(6021,plain,
% 1.63/1.88 (b(s(elem!1), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[826, 32, 610, 6020])).
% 1.63/1.88 tff(6022,plain,
% 1.63/1.88 (((~![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(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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6023,plain,
% 1.63/1.88 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6024,plain,
% 1.63/1.88 (((~![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(z))), 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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[6023])).
% 1.63/1.88 tff(6025,plain,
% 1.63/1.88 (((~![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(z))), 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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[6024, 6022])).
% 1.63/1.88 tff(6026,plain,
% 1.63/1.88 ((~![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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(6027,plain,
% 1.63/1.88 ((~![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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6026, 6025])).
% 1.63/1.88 tff(6028,plain,
% 1.63/1.88 (~r(s(s(s(z))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6027, 141, 2641, 6013])).
% 1.63/1.88 tff(6029,plain,
% 1.63/1.88 (b(s(s(s(z))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[895, 32, 6028, 892])).
% 1.63/1.88 tff(6030,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6031,plain,
% 1.63/1.88 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6032,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[6031])).
% 1.63/1.88 tff(6033,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[6032, 6030])).
% 1.63/1.88 tff(6034,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(6035,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6034, 6033])).
% 1.63/1.88 tff(6036,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6035, 245, 355, 4188, 4187, 6029, 6021])).
% 1.63/1.88 tff(6037,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (s(elem!1) = s(s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(6038,plain,
% 1.63/1.88 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6037, 5970, 355, 5691, 610, 6011, 5994])).
% 1.63/1.88 tff(6039,plain,
% 1.63/1.88 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1515, 6038])).
% 1.63/1.88 tff(6040,plain,
% 1.63/1.88 (((~![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(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6041,plain,
% 1.63/1.88 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(6042,plain,
% 1.63/1.88 (((~![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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[6041])).
% 1.63/1.88 tff(6043,plain,
% 1.63/1.88 (((~![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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[6042, 6040])).
% 1.63/1.88 tff(6044,plain,
% 1.63/1.88 ((~![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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(6045,plain,
% 1.63/1.88 ((~![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(z))))), s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[6044, 6043])).
% 1.63/1.88 tff(6046,plain,
% 1.63/1.88 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[6045, 141, 268, 5959])).
% 1.63/1.88 tff(6047,plain,
% 1.63/1.88 (b(elem!1, s(s(s(s(s(z))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[720, 6046, 5783])).
% 1.63/1.88 tff(6048,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(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(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6049,plain,
% 1.63/1.89 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6050,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[6049])).
% 1.63/1.89 tff(6051,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[6050, 6048])).
% 1.63/1.89 tff(6052,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6053,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6052, 6051])).
% 1.63/1.89 tff(6054,plain,
% 1.63/1.89 (~b(s(s(s(z))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6053, 245, 6047, 5964, 6039, 5986])).
% 1.63/1.89 tff(6055,plain,
% 1.63/1.89 (r(s(s(s(z))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[836, 32, 833, 6054])).
% 1.63/1.89 tff(6056,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~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(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6057,plain,
% 1.63/1.89 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6058,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[6057])).
% 1.63/1.89 tff(6059,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[6058, 6056])).
% 1.63/1.89 tff(6060,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6061,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6060, 6059])).
% 1.63/1.89 tff(6062,plain,
% 1.63/1.89 (~b(s(s(s(z))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6061, 245, 6047, 5964, 6039])).
% 1.63/1.89 tff(6063,plain,
% 1.63/1.89 (((~![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))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6064,plain,
% 1.63/1.89 ((~![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))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6065,plain,
% 1.63/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6064, 6063])).
% 1.63/1.89 tff(6066,plain,
% 1.63/1.89 (r(s(s(s(z))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6065, 32, 6062, 915])).
% 1.63/1.89 tff(6067,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[830, 141, 289, 6066, 6055])).
% 1.63/1.89 tff(6068,plain,((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(z), z)) | (s(elem!1) = s(s(s(z)))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(6069,plain,
% 1.63/1.89 (~r(elem!1, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6068, 5951, 289, 5784, 553, 199, 348, 308, 5925, 5944, 106])).
% 1.63/1.89 tff(6070,plain,
% 1.63/1.89 (b(elem!1, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[281, 6069, 210])).
% 1.63/1.89 tff(6071,plain,
% 1.63/1.89 (~b(s(z), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[5756, 6070, 308, 5925])).
% 1.63/1.89 tff(6072,plain,
% 1.63/1.89 (r(s(z), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[440, 6071, 9])).
% 1.63/1.89 tff(6073,plain,
% 1.63/1.89 (b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6070, 201])).
% 1.63/1.89 tff(6074,plain,
% 1.63/1.89 (~b(z, s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4236, 4188, 355, 10, 2653])).
% 1.63/1.89 tff(6075,plain,
% 1.63/1.89 (r(z, s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[644, 6074])).
% 1.63/1.89 tff(6076,plain,
% 1.63/1.89 (~r(z, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2403, 141, 6075, 486])).
% 1.63/1.89 tff(6077,plain,
% 1.63/1.89 (b(z, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1421, 6076])).
% 1.63/1.89 tff(6078,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6079,plain,
% 1.63/1.89 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6080,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[6079])).
% 1.63/1.89 tff(6081,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[6080, 6078])).
% 1.63/1.89 tff(6082,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6083,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6082, 6081])).
% 1.63/1.89 tff(6084,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6083, 245, 355, 4188, 556, 6077, 2653])).
% 1.63/1.89 tff(6085,plain,((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(6086,plain,
% 1.63/1.89 (~b(s(elem!1), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6085, 6073, 309, 6072, 5951, 10])).
% 1.63/1.89 tff(6087,plain,
% 1.63/1.89 (r(s(elem!1), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[369, 6086, 348])).
% 1.63/1.89 tff(6088,plain,
% 1.63/1.89 (r(s(s(s(elem!1))), s(z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6087, 5949])).
% 1.63/1.89 tff(6089,plain,
% 1.63/1.89 (~r(z, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1457, 6088, 5947])).
% 1.63/1.89 tff(6090,plain,
% 1.63/1.89 (b(z, s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1421, 6089])).
% 1.63/1.89 tff(6091,plain,
% 1.63/1.89 (~b(s(s(s(s(s(z))))), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[5957, 245, 5951, 6090, 5944])).
% 1.63/1.89 tff(6092,plain,
% 1.63/1.89 (r(s(s(s(s(s(z))))), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[809, 6091])).
% 1.63/1.89 tff(6093,plain,
% 1.63/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6094,plain,
% 1.63/1.89 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6095,plain,
% 1.63/1.89 (((~![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(elem!1), s(z))) | (~r(s(elem!1), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[6094])).
% 1.63/1.89 tff(6096,plain,
% 1.63/1.89 (((~![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(elem!1), s(z))) | (~r(s(elem!1), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[6095, 6093])).
% 1.63/1.89 tff(6097,plain,
% 1.63/1.89 ((~![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(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6098,plain,
% 1.63/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6097, 6096])).
% 1.63/1.89 tff(6099,plain,
% 1.63/1.89 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6098, 141, 6087, 6092])).
% 1.63/1.89 tff(6100,plain,
% 1.63/1.89 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6099, 5918])).
% 1.63/1.89 tff(6101,plain,
% 1.63/1.89 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6009, 6100, 5916])).
% 1.63/1.89 tff(6102,plain,
% 1.63/1.89 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6101, 5912])).
% 1.63/1.89 tff(6103,plain,
% 1.63/1.89 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1003, 6092, 6087])).
% 1.63/1.89 tff(6104,plain,
% 1.63/1.89 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[5933, 32, 6103, 5924])).
% 1.63/1.89 tff(6105,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6106,plain,
% 1.63/1.89 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6107,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[6106])).
% 1.63/1.89 tff(6108,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[6107, 6105])).
% 1.63/1.89 tff(6109,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6110,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6109, 6108])).
% 1.63/1.89 tff(6111,plain,
% 1.63/1.89 ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6110, 245, 6070, 308, 5951, 5944])).
% 1.63/1.89 tff(6112,plain,
% 1.63/1.89 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6111, 6104])).
% 1.63/1.89 tff(6113,plain,
% 1.63/1.89 (r(s(s(s(s(s(z))))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[787, 6112, 5814])).
% 1.63/1.89 tff(6114,plain,
% 1.63/1.89 (((~![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(z))))), elem!1)) | (~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, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6115,plain,
% 1.63/1.89 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6116,plain,
% 1.63/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![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(z))))), elem!1)) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[6115])).
% 1.63/1.89 tff(6117,plain,
% 1.63/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![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(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[6116, 6114])).
% 1.63/1.89 tff(6118,plain,
% 1.63/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6119,plain,
% 1.63/1.89 ((~![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(z))))), elem!1)) | (~r(z, s(s(s(s(s(z)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6118, 6117])).
% 1.63/1.89 tff(6120,plain,
% 1.63/1.89 (~r(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6119, 141, 289, 6113])).
% 1.63/1.89 tff(6121,plain,
% 1.63/1.89 (b(z, s(s(s(s(s(z))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[758, 6120])).
% 1.63/1.89 tff(6122,assumption,(b(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.63/1.89 tff(6123,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.63/1.89 tff(6124,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6125,plain,
% 1.63/1.89 (((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(6126,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[6125])).
% 1.63/1.89 tff(6127,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[6126, 6124])).
% 1.63/1.89 tff(6128,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(6129,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[6128, 6127])).
% 1.63/1.89 tff(6130,plain,
% 1.63/1.89 (~b(s(s(s(z))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[6129, 245, 6123, 2222, 4300, 6122])).
% 1.63/1.89 tff(6131,plain,
% 1.63/1.89 (r(s(s(s(z))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[836, 32, 833, 6130])).
% 1.63/1.89 tff(6132,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6133,plain,
% 1.73/1.90 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6134,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[6133])).
% 1.73/1.90 tff(6135,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[6134, 6132])).
% 1.73/1.90 tff(6136,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(6137,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6136, 6135])).
% 1.73/1.90 tff(6138,plain,
% 1.73/1.90 (~b(s(elem!1), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6137, 245, 308, 6123, 4300, 6122])).
% 1.73/1.90 tff(6139,plain,
% 1.73/1.90 (r(s(elem!1), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[826, 32, 610, 6138])).
% 1.73/1.90 tff(6140,plain,
% 1.73/1.90 (((~![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))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6141,plain,
% 1.73/1.90 (((~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))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6142,plain,
% 1.73/1.90 (((~![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)))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[6141])).
% 1.73/1.90 tff(6143,plain,
% 1.73/1.90 (((~![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))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[6142, 6140])).
% 1.73/1.90 tff(6144,plain,
% 1.73/1.90 ((~![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))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(6145,plain,
% 1.73/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6144, 6143])).
% 1.73/1.90 tff(6146,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6145, 141, 1097, 6139, 6131])).
% 1.73/1.90 tff(6147,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(6148,plain,
% 1.73/1.90 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6147, 1097, 5784, 6121, 6104, 6102, 308])).
% 1.73/1.90 tff(6149,plain,
% 1.73/1.90 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1515, 6148])).
% 1.73/1.90 tff(6150,plain,
% 1.73/1.90 (~b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[5992, 245, 5951, 6090, 5944])).
% 1.73/1.90 tff(6151,plain,
% 1.73/1.90 (r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1698, 6150])).
% 1.73/1.90 tff(6152,plain,
% 1.73/1.90 (~r(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6027, 141, 6151, 6149])).
% 1.73/1.90 tff(6153,plain,
% 1.73/1.90 (b(s(s(s(z))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[895, 32, 6152, 892])).
% 1.73/1.90 tff(6154,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6155,plain,
% 1.73/1.90 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6156,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[6155])).
% 1.73/1.90 tff(6157,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[6156, 6154])).
% 1.73/1.90 tff(6158,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(6159,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6158, 6157])).
% 1.73/1.90 tff(6160,plain,
% 1.73/1.90 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6159, 245, 6070, 308, 5925, 6104])).
% 1.73/1.90 tff(6161,plain,
% 1.73/1.90 (r(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[720, 6160, 5783])).
% 1.73/1.90 tff(6162,plain,
% 1.73/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6163,plain,
% 1.73/1.90 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6164,plain,
% 1.73/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[6163])).
% 1.73/1.90 tff(6165,plain,
% 1.73/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[6164, 6162])).
% 1.73/1.90 tff(6166,plain,
% 1.73/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(6167,plain,
% 1.73/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6166, 6165])).
% 1.73/1.90 tff(6168,plain,
% 1.73/1.90 (~r(s(s(s(z))), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6167, 141, 6161, 6149])).
% 1.73/1.90 tff(6169,plain,
% 1.73/1.90 (b(s(s(s(z))), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6065, 32, 6168, 915])).
% 1.73/1.90 tff(6170,plain,
% 1.73/1.90 (~r(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2649, 6113, 6151])).
% 1.73/1.90 tff(6171,plain,
% 1.73/1.90 (b(s(z), elem!1)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[389, 6170, 342])).
% 1.73/1.90 tff(6172,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6173,plain,
% 1.73/1.90 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6174,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[6173])).
% 1.73/1.90 tff(6175,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/1.90 inference(transitivity,[status(thm)],[6174, 6172])).
% 1.73/1.90 tff(6176,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(6177,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6176, 6175])).
% 1.73/1.90 tff(6178,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6177, 245, 308, 5925, 6171, 6169, 6153])).
% 1.73/1.90 tff(6179,plain,((~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(6180,plain,
% 1.73/1.90 (~r(s(elem!1), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6179, 5623, 5774, 152, 176, 5906, 9, 106, 129])).
% 1.73/1.90 tff(6181,plain,
% 1.73/1.90 (b(s(elem!1), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1039, 6180])).
% 1.73/1.90 tff(6182,plain,
% 1.73/1.90 (~r(elem!1, s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4612, 4180, 402])).
% 1.73/1.90 tff(6183,plain,
% 1.73/1.90 (b(elem!1, s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[281, 6182, 210])).
% 1.73/1.90 tff(6184,plain,
% 1.73/1.90 (~b(s(elem!1), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[5723, 245, 6183, 308, 5512])).
% 1.73/1.90 tff(6185,plain,
% 1.73/1.90 (r(s(elem!1), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[369, 6184, 348])).
% 1.73/1.90 tff(6186,plain,
% 1.73/1.90 (~b(s(z), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[5756, 6183, 308, 1103])).
% 1.73/1.90 tff(6187,plain,
% 1.73/1.90 (r(s(z), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[440, 6186, 9])).
% 1.73/1.90 tff(6188,plain,
% 1.73/1.90 (((~![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(z))))), elem!1)) | (~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, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6189,plain,
% 1.73/1.90 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(6190,plain,
% 1.73/1.90 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6189, 6188])).
% 1.73/1.90 tff(6191,plain,
% 1.73/1.90 (~r(s(s(s(s(s(z))))), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6190, 141, 289, 2628])).
% 1.73/1.90 tff(6192,plain,
% 1.73/1.90 (b(s(s(s(s(s(z))))), z)),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[738, 6191])).
% 1.73/1.90 tff(6193,plain,
% 1.73/1.90 (~r(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6119, 141, 289, 2628])).
% 1.73/1.90 tff(6194,plain,
% 1.73/1.90 (b(z, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[758, 6193])).
% 1.73/1.90 tff(6195,plain,
% 1.73/1.90 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[5797, 245, 288, 6194, 6192])).
% 1.73/1.90 tff(6196,plain,
% 1.73/1.90 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6195, 676])).
% 1.73/1.90 tff(6197,plain,
% 1.73/1.90 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[797, 6196, 917])).
% 1.73/1.90 tff(6198,plain,
% 1.73/1.90 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6197, 5780])).
% 1.73/1.90 tff(6199,plain,
% 1.73/1.90 (~r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[5835, 141, 486, 6198])).
% 1.73/1.90 tff(6200,plain,
% 1.73/1.90 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[809, 6199])).
% 1.73/1.90 tff(6201,plain,
% 1.73/1.90 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[715, 245, 301, 447, 6200])).
% 1.73/1.90 tff(6202,plain,
% 1.73/1.90 (r(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[720, 6201, 5783])).
% 1.73/1.90 tff(6203,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6204,plain,
% 1.73/1.90 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(6205,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[6204])).
% 1.73/1.90 tff(6206,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[6205, 6203])).
% 1.73/1.90 tff(6207,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(6208,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6207, 6206])).
% 1.73/1.90 tff(6209,plain,
% 1.73/1.90 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6208, 245, 288, 6194, 6192])).
% 1.73/1.90 tff(6210,plain,
% 1.73/1.90 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[6209, 5997])).
% 1.73/1.90 tff(6211,plain,
% 1.73/1.90 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[6009, 6210, 5996])).
% 1.73/1.91 tff(6212,plain,
% 1.73/1.91 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6211, 5995])).
% 1.73/1.91 tff(6213,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.73/1.91 tff(6214,plain,
% 1.73/1.91 (~r(s(s(s(z))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6167, 141, 723, 6013])).
% 1.73/1.91 tff(6215,plain,
% 1.73/1.91 (b(s(s(s(z))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6065, 32, 6214, 6213])).
% 1.73/1.91 tff(6216,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6217,plain,
% 1.73/1.91 (((~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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6218,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[6217])).
% 1.73/1.91 tff(6219,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[6218, 6216])).
% 1.73/1.91 tff(6220,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(6221,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6220, 6219])).
% 1.73/1.91 tff(6222,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6221, 245, 301, 308, 447, 6215, 6021])).
% 1.73/1.91 tff(6223,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(s(s(z)))) | (s(s(s(z))) = elem!1) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(6224,plain,
% 1.73/1.91 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6223, 6212, 308, 447, 610, 915, 301, 6202])).
% 1.73/1.91 tff(6225,plain,
% 1.73/1.91 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1515, 6224])).
% 1.73/1.91 tff(6226,plain,
% 1.73/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~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(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6227,plain,
% 1.73/1.91 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6228,plain,
% 1.73/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[6227])).
% 1.73/1.91 tff(6229,plain,
% 1.73/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[6228, 6226])).
% 1.73/1.91 tff(6230,plain,
% 1.73/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(6231,plain,
% 1.73/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6230, 6229])).
% 1.73/1.91 tff(6232,plain,
% 1.73/1.91 (~r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6231, 141, 486, 6198])).
% 1.73/1.91 tff(6233,plain,
% 1.73/1.91 (b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1698, 6232])).
% 1.73/1.91 tff(6234,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6235,plain,
% 1.73/1.91 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6236,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[6235])).
% 1.73/1.91 tff(6237,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[6236, 6234])).
% 1.73/1.91 tff(6238,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(6239,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6238, 6237])).
% 1.73/1.91 tff(6240,plain,
% 1.73/1.91 (~b(s(s(s(z))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6239, 245, 6233, 6225, 6200])).
% 1.73/1.91 tff(6241,plain,
% 1.73/1.91 (r(s(s(s(z))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[895, 32, 892, 6240])).
% 1.73/1.91 tff(6242,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(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(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6243,plain,
% 1.73/1.91 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6244,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[6243])).
% 1.73/1.91 tff(6245,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[6244, 6242])).
% 1.73/1.91 tff(6246,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(6247,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6246, 6245])).
% 1.73/1.91 tff(6248,plain,
% 1.73/1.91 (~b(s(s(s(z))), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6247, 245, 6233, 6225, 6194, 6200])).
% 1.73/1.91 tff(6249,plain,
% 1.73/1.91 (r(s(s(s(z))), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[836, 32, 833, 6248])).
% 1.73/1.91 tff(6250,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[985, 6249, 6241, 220])).
% 1.73/1.91 tff(6251,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(s(s(z)))) | (~b(elem!1, s(z))) | (~r(s(z), s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(elem!1), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(6252,plain,
% 1.73/1.91 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6251, 220, 308, 5512, 5784, 6183, 6187, 553, 199, 288, 289])).
% 1.73/1.91 tff(6253,plain,
% 1.73/1.91 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[787, 6252, 5814])).
% 1.73/1.91 tff(6254,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6255,plain,
% 1.73/1.91 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6256,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[6255])).
% 1.73/1.91 tff(6257,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.91 inference(transitivity,[status(thm)],[6256, 6254])).
% 1.73/1.91 tff(6258,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(6259,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 1.73/1.91 tff(6260,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6259, 245, 308, 1103, 5512, 6253])).
% 1.73/1.91 tff(6261,plain,
% 1.73/1.91 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[809, 6260])).
% 1.73/1.91 tff(6262,plain,
% 1.73/1.91 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1003, 6261, 6185])).
% 1.73/1.91 tff(6263,plain,
% 1.73/1.91 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6262, 5782])).
% 1.73/1.91 tff(6264,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[5940, 245, 308, 1103, 6253])).
% 1.73/1.91 tff(6265,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6264, 676])).
% 1.73/1.91 tff(6266,plain,
% 1.73/1.91 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[797, 6265, 5785])).
% 1.73/1.91 tff(6267,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6266, 6263])).
% 1.73/1.91 tff(6268,plain,((~r(s(z), z)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(6269,plain,
% 1.73/1.91 (~r(s(z), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6268, 553, 199, 308, 1103, 288, 289, 131, 9, 106])).
% 1.73/1.91 tff(6270,plain,
% 1.73/1.91 (b(s(z), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[232, 6269])).
% 1.73/1.91 tff(6271,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6068, 268, 289, 5784, 553, 199, 348, 308, 1103, 6270, 106])).
% 1.73/1.91 tff(6272,plain,
% 1.73/1.91 (r(s(s(s(s(s(z))))), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[738, 6271])).
% 1.73/1.91 tff(6273,plain,
% 1.73/1.91 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1161, 141, 131, 6272])).
% 1.73/1.91 tff(6274,plain,
% 1.73/1.91 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[787, 6273, 5814])).
% 1.73/1.91 tff(6275,plain,
% 1.73/1.91 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6003, 245, 308, 1103, 6274])).
% 1.73/1.91 tff(6276,plain,
% 1.73/1.91 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6275, 5997])).
% 1.73/1.91 tff(6277,plain,
% 1.73/1.91 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6009, 6276, 5916])).
% 1.73/1.91 tff(6278,plain,
% 1.73/1.91 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6277, 5995])).
% 1.73/1.91 tff(6279,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[5940, 245, 308, 1103, 6274])).
% 1.73/1.91 tff(6280,plain,
% 1.73/1.91 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6279, 676])).
% 1.73/1.91 tff(6281,plain,
% 1.73/1.91 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[797, 6280, 5785])).
% 1.73/1.91 tff(6282,plain,
% 1.73/1.91 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6281, 5780])).
% 1.73/1.91 tff(6283,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), z)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6284,plain,
% 1.73/1.91 (((~b(s(z), z)) | (~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), s(elem!1))) | (~b(s(z), z)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(6285,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(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(X0, 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), s(elem!1))) | (~b(s(z), z))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[6284])).
% 1.73/1.91 tff(6286,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(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(X0, 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), s(elem!1))) | (~b(s(z), z)))),
% 1.73/1.91 inference(transitivity,[status(thm)],[6285, 6283])).
% 1.73/1.91 tff(6287,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(6288,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(elem!1))) | (~b(s(z), z))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[6287, 6286])).
% 1.73/1.91 tff(6289,plain,
% 1.73/1.91 (~b(s(z), s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6288, 245, 6270, 288, 5691])).
% 1.73/1.91 tff(6290,plain,
% 1.73/1.91 (r(s(z), s(elem!1))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[440, 6289, 9])).
% 1.73/1.91 tff(6291,plain,
% 1.73/1.91 (~r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[6231, 141, 6290, 6282])).
% 1.73/1.91 tff(6292,plain,
% 1.73/1.91 (b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1698, 6291])).
% 1.73/1.91 tff(6293,plain,
% 1.73/1.91 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[731, 6272, 131])).
% 1.73/1.91 tff(6294,plain,
% 1.73/1.91 (b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[720, 6293, 5783])).
% 1.73/1.91 tff(6295,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6296,plain,
% 1.73/1.92 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6297,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6296])).
% 1.73/1.92 tff(6298,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.92 inference(transitivity,[status(thm)],[6297, 6295])).
% 1.73/1.92 tff(6299,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(6300,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6299, 6298])).
% 1.73/1.92 tff(6301,plain,
% 1.73/1.92 ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6300, 245, 1103, 6270, 288, 6274])).
% 1.73/1.92 tff(6302,plain,
% 1.73/1.92 (~b(s(z), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6301, 6292])).
% 1.73/1.92 tff(6303,plain,
% 1.73/1.92 (r(s(z), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[389, 6302, 342])).
% 1.73/1.92 tff(6304,plain,
% 1.73/1.92 (~b(s(s(s(z))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6061, 245, 5823, 4878, 6123])).
% 1.73/1.92 tff(6305,plain,
% 1.73/1.92 (r(s(s(s(z))), elem!1)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6065, 32, 6304, 6213])).
% 1.73/1.92 tff(6306,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.73/1.92 tff(6307,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~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(X0, 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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6308,plain,
% 1.73/1.92 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(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(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6309,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6308])).
% 1.73/1.92 tff(6310,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[6309, 6307])).
% 1.73/1.92 tff(6311,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(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(z))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(6312,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6311, 6310])).
% 1.73/1.92 tff(6313,plain,
% 1.73/1.92 (~b(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6312, 245, 5823, 6306, 4878, 6123])).
% 1.73/1.92 tff(6314,plain,
% 1.73/1.92 (r(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[895, 32, 892, 6313])).
% 1.73/1.92 tff(6315,plain,
% 1.73/1.92 (((~![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))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6316,plain,
% 1.73/1.92 ((~![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))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(6317,plain,
% 1.73/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 1.73/1.92 tff(6318,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6317, 141, 619, 6314, 6305])).
% 1.73/1.92 tff(6319,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(6320,plain,
% 1.73/1.92 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6319, 6303, 915, 6294, 6292, 6274])).
% 1.73/1.92 tff(6321,plain,
% 1.73/1.92 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1515, 6320])).
% 1.73/1.92 tff(6322,plain,
% 1.73/1.92 (~r(s(elem!1), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6019, 141, 6321, 6278])).
% 1.73/1.92 tff(6323,plain,
% 1.73/1.92 (b(s(elem!1), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[826, 32, 5784, 6322])).
% 1.73/1.92 tff(6324,plain,
% 1.73/1.92 (~r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5835, 141, 6290, 6282])).
% 1.73/1.92 tff(6325,plain,
% 1.73/1.92 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[809, 6324])).
% 1.73/1.92 tff(6326,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6327,plain,
% 1.73/1.92 (((~b(z, s(z))) | (~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))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6328,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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(X0, 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)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6327])).
% 1.73/1.92 tff(6329,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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(X0, 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))))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[6328, 6326])).
% 1.73/1.92 tff(6330,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(6331,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6330, 6329])).
% 1.73/1.92 tff(6332,plain,
% 1.73/1.92 (~b(z, s(s(s(s(s(z))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6331, 245, 6270, 5691, 6325])).
% 1.73/1.92 tff(6333,plain,
% 1.73/1.92 (r(z, s(s(s(s(s(z))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[758, 6332])).
% 1.73/1.92 tff(6334,plain,
% 1.73/1.92 (((~![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(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6335,plain,
% 1.73/1.92 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6336,plain,
% 1.73/1.92 (((~![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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6335])).
% 1.73/1.92 tff(6337,plain,
% 1.73/1.92 (((~![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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[6336, 6334])).
% 1.73/1.92 tff(6338,plain,
% 1.73/1.92 ((~![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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(6339,plain,
% 1.73/1.92 ((~![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(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6338, 6337])).
% 1.73/1.92 tff(6340,plain,
% 1.73/1.92 (~r(s(s(s(z))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6339, 141, 6321, 6333])).
% 1.73/1.92 tff(6341,plain,
% 1.73/1.92 (b(s(s(s(z))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[836, 32, 833, 6340])).
% 1.73/1.92 tff(6342,plain,
% 1.73/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6343,plain,
% 1.73/1.92 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6344,plain,
% 1.73/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6343])).
% 1.73/1.92 tff(6345,plain,
% 1.73/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[6344, 6342])).
% 1.73/1.92 tff(6346,plain,
% 1.73/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(elem!1))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(6347,plain,
% 1.73/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6346, 6345])).
% 1.73/1.92 tff(6348,plain,
% 1.73/1.92 (~r(z, s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6347, 141, 6333, 6278])).
% 1.73/1.92 tff(6349,plain,
% 1.73/1.92 (b(z, s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[644, 6348])).
% 1.73/1.92 tff(6350,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6351,plain,
% 1.73/1.92 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~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), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6352,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6351])).
% 1.73/1.92 tff(6353,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[6352, 6350])).
% 1.73/1.92 tff(6354,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(6355,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6354, 6353])).
% 1.73/1.92 tff(6356,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6355, 245, 308, 288, 6349, 6341, 6323])).
% 1.73/1.92 tff(6357,plain,((~r(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(z) = s(elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(6358,plain,
% 1.73/1.92 (~r(elem!1, s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6357, 5623, 6181, 5908, 5774, 152, 9, 129, 106, 176])).
% 1.73/1.92 tff(6359,plain,
% 1.73/1.92 (b(elem!1, s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[281, 6358, 5910])).
% 1.73/1.92 tff(6360,plain,
% 1.73/1.92 (~b(s(z), s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[5756, 6359, 5623, 5908])).
% 1.73/1.92 tff(6361,plain,
% 1.73/1.92 (r(s(z), s(elem!1))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[440, 6360, 9])).
% 1.73/1.92 tff(6362,plain,
% 1.73/1.92 (~r(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6268, 5774, 152, 5623, 5908, 6181, 176, 129, 9, 106])).
% 1.73/1.92 tff(6363,plain,
% 1.73/1.92 (b(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[232, 6362])).
% 1.73/1.92 tff(6364,plain,
% 1.73/1.92 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), elem!1)),
% 1.73/1.92 inference(monotonicity,[status(thm)],[152])).
% 1.73/1.92 tff(6365,plain,
% 1.73/1.92 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.92 inference(symmetry,[status(thm)],[6364])).
% 1.73/1.92 tff(6366,plain,
% 1.73/1.92 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[5623, 6365])).
% 1.73/1.92 tff(6367,plain,
% 1.73/1.92 (b(elem!1, s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.73/1.92 inference(symmetry,[status(thm)],[171])).
% 1.73/1.92 tff(6368,plain,
% 1.73/1.92 (b(s(s(s(s(elem!1)))), s(z))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6359, 6367])).
% 1.73/1.92 tff(6369,plain,
% 1.73/1.92 (~b(s(elem!1), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[6085, 6368, 6366, 6363, 6361, 5906])).
% 1.73/1.92 tff(6370,plain,
% 1.73/1.92 (r(s(elem!1), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[369, 6369, 348])).
% 1.73/1.92 tff(6371,plain,
% 1.73/1.92 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[594, 5774, 152, 9])).
% 1.73/1.92 tff(6372,plain,
% 1.73/1.92 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[612, 5774, 152, 6371])).
% 1.73/1.92 tff(6373,plain,
% 1.73/1.92 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.73/1.92 inference(monotonicity,[status(thm)],[5774])).
% 1.73/1.92 tff(6374,plain,
% 1.73/1.92 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 1.73/1.92 inference(symmetry,[status(thm)],[6373])).
% 1.73/1.92 tff(6375,plain,
% 1.73/1.92 ((~r(s(elem!1), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6374])).
% 1.73/1.92 tff(6376,plain,
% 1.73/1.92 (~r(s(s(s(elem!1))), z)),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6180, 6375])).
% 1.73/1.92 tff(6377,plain,
% 1.73/1.92 (b(s(s(s(elem!1))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[37, 6376])).
% 1.73/1.92 tff(6378,plain,
% 1.73/1.92 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[5774])).
% 1.73/1.92 tff(6379,plain,
% 1.73/1.92 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.73/1.92 inference(symmetry,[status(thm)],[6378])).
% 1.73/1.92 tff(6380,plain,
% 1.73/1.92 (r(s(s(s(elem!1))), s(z))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[6370, 6379])).
% 1.73/1.92 tff(6381,plain,
% 1.73/1.92 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[614])).
% 1.73/1.92 tff(6382,plain,
% 1.73/1.92 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.92 inference(symmetry,[status(thm)],[6381])).
% 1.73/1.92 tff(6383,plain,
% 1.73/1.92 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[614])).
% 1.73/1.92 tff(6384,plain,
% 1.73/1.92 ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6383])).
% 1.73/1.92 tff(6385,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6386,plain,
% 1.73/1.92 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(6387,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[6386])).
% 1.73/1.92 tff(6388,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[6387, 6385])).
% 1.73/1.93 tff(6389,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6390,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6389, 6388])).
% 1.73/1.93 tff(6391,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6390, 245, 234, 5789, 5787])).
% 1.73/1.93 tff(6392,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6391, 6384])).
% 1.73/1.93 tff(6393,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[797, 6392, 673])).
% 1.73/1.93 tff(6394,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6393, 6382])).
% 1.73/1.93 tff(6395,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6396,plain,
% 1.73/1.93 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6397,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6396])).
% 1.73/1.93 tff(6398,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[6397, 6395])).
% 1.73/1.93 tff(6399,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6400,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6399, 6398])).
% 1.73/1.93 tff(6401,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6400, 245, 355, 5789, 5787])).
% 1.73/1.93 tff(6402,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[809, 6401])).
% 1.73/1.93 tff(6403,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1196, 141, 267, 6402])).
% 1.73/1.93 tff(6404,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6403, 6394])).
% 1.73/1.93 tff(6405,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6406,plain,
% 1.73/1.93 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6405, 6380, 152, 6372, 6377, 6363, 129, 176])).
% 1.73/1.93 tff(6407,plain,
% 1.73/1.93 (b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[720, 6406, 1052])).
% 1.73/1.93 tff(6408,plain,
% 1.73/1.93 (s(s(s(s(elem!1)))) = elem!1),
% 1.73/1.93 inference(symmetry,[status(thm)],[422])).
% 1.73/1.93 tff(6409,plain,
% 1.73/1.93 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), elem!1)),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6408])).
% 1.73/1.93 tff(6410,plain,
% 1.73/1.93 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(symmetry,[status(thm)],[6409])).
% 1.73/1.93 tff(6411,plain,
% 1.73/1.93 (r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[619, 6410])).
% 1.73/1.93 tff(6412,plain,
% 1.73/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6413,plain,
% 1.73/1.93 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6414,plain,
% 1.73/1.93 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6413])).
% 1.73/1.93 tff(6415,plain,
% 1.73/1.93 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[6414, 6412])).
% 1.73/1.93 tff(6416,plain,
% 1.73/1.93 ((~![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(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6417,plain,
% 1.73/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6416, 6415])).
% 1.73/1.93 tff(6418,plain,
% 1.73/1.93 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6417, 141, 310, 1449])).
% 1.73/1.93 tff(6419,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6418, 6411])).
% 1.73/1.93 tff(6420,plain,((~r(s(z), elem!1)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6421,plain,
% 1.73/1.93 (~r(z, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6420, 619, 402, 304])).
% 1.73/1.93 tff(6422,plain,
% 1.73/1.93 (b(z, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1421, 6421])).
% 1.73/1.93 tff(6423,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5992, 245, 355, 4187, 2651, 6192])).
% 1.73/1.93 tff(6424,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6425,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6424, 6422, 355, 289, 619])).
% 1.73/1.93 tff(6426,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[787, 6425, 5814])).
% 1.73/1.93 tff(6427,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5940, 245, 308, 1103, 6426])).
% 1.73/1.93 tff(6428,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6427, 676])).
% 1.73/1.93 tff(6429,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[797, 6428, 673])).
% 1.73/1.93 tff(6430,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6429, 5780])).
% 1.73/1.93 tff(6431,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5835, 141, 486, 6430])).
% 1.73/1.93 tff(6432,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[809, 6431])).
% 1.73/1.93 tff(6433,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6434,plain,
% 1.73/1.93 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6435,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6434])).
% 1.73/1.93 tff(6436,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[6435, 6433])).
% 1.73/1.93 tff(6437,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6438,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6437, 6436])).
% 1.73/1.93 tff(6439,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6438, 245, 301, 355, 6422, 5823, 6432])).
% 1.73/1.93 tff(6440,plain,((~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6441,plain,
% 1.73/1.93 (~r(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6440, 6359, 6363, 6407, 6361, 5774, 152, 6372, 5623, 5908, 176])).
% 1.73/1.93 tff(6442,plain,
% 1.73/1.93 (b(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[389, 6441, 1070])).
% 1.73/1.93 tff(6443,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6259, 245, 308, 1103, 447, 4878])).
% 1.73/1.93 tff(6444,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[809, 6443])).
% 1.73/1.93 tff(6445,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1003, 6444, 998])).
% 1.73/1.93 tff(6446,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6445, 5782])).
% 1.73/1.93 tff(6447,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5940, 245, 308, 1103, 4878])).
% 1.73/1.93 tff(6448,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6447, 676])).
% 1.73/1.93 tff(6449,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[797, 6448, 673])).
% 1.73/1.93 tff(6450,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6449, 6446])).
% 1.73/1.93 tff(6451,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6452,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6451, 5774, 152, 6372, 6370, 5623, 5908, 6442])).
% 1.73/1.93 tff(6453,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[787, 6452, 1053])).
% 1.73/1.93 tff(6454,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6190, 141, 176, 6453])).
% 1.73/1.93 tff(6455,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[738, 6454])).
% 1.73/1.93 tff(6456,plain,
% 1.73/1.93 (~r(z, s(s(s(s(s(z))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6119, 141, 176, 6453])).
% 1.73/1.93 tff(6457,plain,
% 1.73/1.93 (b(z, s(s(s(s(s(z))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[758, 6456])).
% 1.73/1.93 tff(6458,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6400, 245, 6363, 6457, 6455])).
% 1.73/1.93 tff(6459,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[809, 6458])).
% 1.73/1.93 tff(6460,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1003, 6459, 6370])).
% 1.73/1.93 tff(6461,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6460, 5778])).
% 1.73/1.93 tff(6462,plain,
% 1.73/1.93 (s(elem!1) = s(s(s(elem!1)))),
% 1.73/1.93 inference(symmetry,[status(thm)],[5774])).
% 1.73/1.93 tff(6463,plain,
% 1.73/1.93 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[6462, 161])).
% 1.73/1.93 tff(6464,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6463])).
% 1.73/1.93 tff(6465,plain,
% 1.73/1.93 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6464])).
% 1.73/1.93 tff(6466,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5797, 245, 6181, 6457, 6455])).
% 1.73/1.93 tff(6467,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6466, 6465])).
% 1.73/1.93 tff(6468,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[797, 6467, 6372])).
% 1.73/1.93 tff(6469,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6468, 6461])).
% 1.73/1.93 tff(6470,plain,((s(z) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6471,plain,
% 1.73/1.93 (~r(s(s(s(s(elem!1)))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6470, 89, 1, 5466, 5461, 90])).
% 1.73/1.93 tff(6472,plain,
% 1.73/1.93 (~b(s(s(s(s(elem!1)))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1949, 89, 199])).
% 1.73/1.93 tff(6473,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2558, 6472, 6471])).
% 1.73/1.93 tff(6474,plain,(b(elem!1, z) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6475,plain,
% 1.73/1.93 (b(elem!1, z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6474, 90, 1, 199])).
% 1.73/1.93 tff(6476,plain,
% 1.73/1.93 (r(z, elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[175, 90, 5465])).
% 1.73/1.93 tff(6477,plain,
% 1.73/1.93 (~r(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[670, 289, 572, 5466])).
% 1.73/1.93 tff(6478,plain,
% 1.73/1.93 (b(s(z), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[389, 6477, 342])).
% 1.73/1.93 tff(6479,plain,
% 1.73/1.93 (~r(s(s(s(elem!1))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2875, 170, 289])).
% 1.73/1.93 tff(6480,plain,
% 1.73/1.93 (b(s(s(s(elem!1))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[37, 6479])).
% 1.73/1.93 tff(6481,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6482,plain,
% 1.73/1.93 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6483,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6482])).
% 1.73/1.93 tff(6484,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[6483, 6481])).
% 1.73/1.93 tff(6485,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6486,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6485, 6484])).
% 1.73/1.93 tff(6487,plain,
% 1.73/1.93 (~b(elem!1, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6486, 245, 4186, 447, 4187])).
% 1.73/1.93 tff(6488,plain,
% 1.73/1.93 (r(elem!1, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[281, 6487, 3599])).
% 1.73/1.93 tff(6489,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6490,plain,
% 1.73/1.93 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6491,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6490])).
% 1.73/1.93 tff(6492,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[6491, 6489])).
% 1.73/1.93 tff(6493,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6494,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6493, 6492])).
% 1.73/1.93 tff(6495,plain,
% 1.73/1.93 (~b(s(s(s(elem!1))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6494, 245, 4186, 234, 447, 4187])).
% 1.73/1.93 tff(6496,plain,
% 1.73/1.93 (r(s(s(s(elem!1))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[265, 6495])).
% 1.73/1.93 tff(6497,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[276, 6496, 6488, 170])).
% 1.73/1.93 tff(6498,plain,((~b(z, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6499,plain,
% 1.73/1.93 (~b(z, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6498, 170, 210, 4186, 6480, 6478])).
% 1.73/1.93 tff(6500,plain,
% 1.73/1.93 (r(z, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1421, 6499])).
% 1.73/1.93 tff(6501,plain,
% 1.73/1.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[577, 170, 572])).
% 1.73/1.93 tff(6502,plain,
% 1.73/1.93 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[299, 245, 293, 6480, 2938])).
% 1.73/1.93 tff(6503,plain,
% 1.73/1.93 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[353, 6502, 6501])).
% 1.73/1.93 tff(6504,plain,
% 1.73/1.93 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[594, 6503, 199, 5466])).
% 1.73/1.93 tff(6505,plain,
% 1.73/1.93 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[612, 6503, 199, 6504])).
% 1.73/1.93 tff(6506,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(symmetry,[status(thm)],[6383])).
% 1.73/1.93 tff(6507,plain,
% 1.73/1.93 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[6381])).
% 1.73/1.93 tff(6508,plain,
% 1.73/1.93 (((~![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(z))))), elem!1)) | (~r(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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6509,plain,
% 1.73/1.93 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6510,plain,
% 1.73/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6509, 6508])).
% 1.73/1.93 tff(6511,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6510, 141, 170, 2628])).
% 1.73/1.93 tff(6512,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6511, 6507])).
% 1.73/1.93 tff(6513,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[797, 6512, 673])).
% 1.73/1.93 tff(6514,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6513, 6506])).
% 1.73/1.93 tff(6515,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1179, 245, 293, 6480, 6192])).
% 1.73/1.93 tff(6516,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6515, 6514])).
% 1.73/1.93 tff(6517,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(6518,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6517, 6505, 199, 170, 289])).
% 1.73/1.93 tff(6519,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[787, 6518, 5814])).
% 1.73/1.93 tff(6520,plain,
% 1.73/1.93 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[5889, 245, 301, 447, 4878])).
% 1.73/1.93 tff(6521,plain,
% 1.73/1.93 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[809, 6520])).
% 1.73/1.93 tff(6522,plain,
% 1.73/1.93 (((~![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)))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(6523,plain,
% 1.73/1.93 ((~![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)))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(6524,plain,
% 1.73/1.93 ((~![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))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[6523, 6522])).
% 1.73/1.93 tff(6525,plain,
% 1.73/1.93 (~r(s(s(s(s(s(z))))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[6524, 141, 1449, 6521])).
% 1.73/1.93 tff(6526,plain,
% 1.73/1.93 (b(s(s(s(s(s(z))))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[738, 6525])).
% 1.73/1.93 tff(6527,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6528,plain,
% 1.73/1.94 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6529,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6528])).
% 1.73/1.94 tff(6530,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.94 inference(transitivity,[status(thm)],[6529, 6527])).
% 1.73/1.94 tff(6531,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6532,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6531, 6530])).
% 1.73/1.94 tff(6533,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6532, 245, 4186, 235, 234, 4878, 6526])).
% 1.73/1.94 tff(6534,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(6535,plain,
% 1.73/1.94 (~b(elem!1, s(z))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6534, 6500, 293, 6480, 4186, 6519, 6478])).
% 1.73/1.94 tff(6536,plain,
% 1.73/1.94 (r(elem!1, s(z))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[281, 6535, 210])).
% 1.73/1.94 tff(6537,plain,
% 1.73/1.94 (((~![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))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6538,plain,
% 1.73/1.94 (((~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))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6539,plain,
% 1.73/1.94 (((~![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)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6538])).
% 1.73/1.94 tff(6540,plain,
% 1.73/1.94 (((~![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))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[6539, 6537])).
% 1.73/1.94 tff(6541,plain,
% 1.73/1.94 ((~![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)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6542,plain,
% 1.73/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6541, 6540])).
% 1.73/1.94 tff(6543,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6542, 141, 289, 6536, 6500])).
% 1.73/1.94 tff(6544,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~b(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(6545,plain,
% 1.73/1.94 (~r(s(s(s(elem!1))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6544, 6476, 6475, 199, 572])).
% 1.73/1.94 tff(6546,plain,
% 1.73/1.94 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[110, 6545, 96])).
% 1.73/1.94 tff(6547,plain,
% 1.73/1.94 (~r(s(z), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[670, 6476, 572, 5466])).
% 1.73/1.94 tff(6548,plain,
% 1.73/1.94 (b(s(z), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[389, 6547, 342])).
% 1.73/1.94 tff(6549,plain,
% 1.73/1.94 (~r(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2078, 2069, 289])).
% 1.73/1.94 tff(6550,plain,
% 1.73/1.94 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1724, 6549, 1717])).
% 1.73/1.94 tff(6551,plain,
% 1.73/1.94 (~b(s(z), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2993, 245, 1427, 447, 6550])).
% 1.73/1.94 tff(6552,plain,
% 1.73/1.94 (r(s(z), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1133, 6551])).
% 1.73/1.94 tff(6553,plain,
% 1.73/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6554,plain,
% 1.73/1.94 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6555,plain,
% 1.73/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6554])).
% 1.73/1.94 tff(6556,plain,
% 1.73/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[6555, 6553])).
% 1.73/1.94 tff(6557,plain,
% 1.73/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6558,plain,
% 1.73/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6557, 6556])).
% 1.73/1.94 tff(6559,plain,
% 1.73/1.94 (~r(z, s(z))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6558, 141, 6552, 2069])).
% 1.73/1.94 tff(6560,plain,
% 1.73/1.94 (b(z, s(z))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1421, 6559])).
% 1.73/1.94 tff(6561,plain,
% 1.73/1.94 (((~![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), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6562,plain,
% 1.73/1.94 ((~![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)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6563,plain,
% 1.73/1.94 ((~![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))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6562, 6561])).
% 1.73/1.94 tff(6564,plain,
% 1.73/1.94 (~r(s(z), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6563, 141, 6552, 2069])).
% 1.73/1.94 tff(6565,plain,
% 1.73/1.94 (b(s(z), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[232, 6564])).
% 1.73/1.94 tff(6566,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6567,plain,
% 1.73/1.94 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6568,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6567])).
% 1.73/1.94 tff(6569,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(transitivity,[status(thm)],[6568, 6566])).
% 1.73/1.94 tff(6570,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6571,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6570, 6569])).
% 1.73/1.94 tff(6572,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6571, 245, 4186, 6565, 447, 6560])).
% 1.73/1.94 tff(6573,plain,((~r(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(6574,plain,
% 1.73/1.94 (~r(z, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6573, 6475, 6548, 6546, 1673, 6476])).
% 1.73/1.94 tff(6575,plain,
% 1.73/1.94 (b(z, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[197, 6574])).
% 1.73/1.94 tff(6576,plain,
% 1.73/1.94 (~b(s(s(s(elem!1))), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4562, 6575, 6475, 6546])).
% 1.73/1.94 tff(6577,plain,
% 1.73/1.94 (r(s(s(s(elem!1))), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[37, 6576])).
% 1.73/1.94 tff(6578,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6579,plain,
% 1.73/1.94 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6580,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6579])).
% 1.73/1.94 tff(6581,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(transitivity,[status(thm)],[6580, 6578])).
% 1.73/1.94 tff(6582,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6583,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6582, 6581])).
% 1.73/1.94 tff(6584,plain,
% 1.73/1.94 (~b(s(z), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6583, 245, 6475, 6546, 6575, 6548])).
% 1.73/1.94 tff(6585,plain,
% 1.73/1.94 (r(s(z), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[232, 6584])).
% 1.73/1.94 tff(6586,plain,
% 1.73/1.94 (~r(s(z), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2109, 6585, 6577])).
% 1.73/1.94 tff(6587,plain,
% 1.73/1.94 (b(s(z), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1133, 6586])).
% 1.73/1.94 tff(6588,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6589,plain,
% 1.73/1.94 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6590,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6589])).
% 1.73/1.94 tff(6591,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[6590, 6588])).
% 1.73/1.94 tff(6592,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6593,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6592, 6591])).
% 1.73/1.94 tff(6594,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6593, 245, 6475, 6546, 6575, 6548, 6587])).
% 1.73/1.94 tff(6595,plain,(b(z, elem!1) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(6596,plain,
% 1.73/1.94 (b(z, elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6595, 5447, 1277, 1])).
% 1.73/1.94 tff(6597,plain,
% 1.73/1.94 (~(s(elem!1) = s(z))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[347, 5466])).
% 1.73/1.94 tff(6598,plain,
% 1.73/1.94 (r(s(s(s(s(elem!1)))), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2558, 6472])).
% 1.73/1.94 tff(6599,plain,
% 1.73/1.94 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = z)),
% 1.73/1.94 inference(transitivity,[status(thm)],[5463, 3639])).
% 1.73/1.94 tff(6600,plain,
% 1.73/1.94 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = z))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6599])).
% 1.73/1.94 tff(6601,plain,
% 1.73/1.94 (~(elem!1 = z)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[66, 6600])).
% 1.73/1.94 tff(6602,plain,
% 1.73/1.94 (r(elem!1, z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[128, 89, 6601])).
% 1.73/1.94 tff(6603,plain,
% 1.73/1.94 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[5564])).
% 1.73/1.94 tff(6604,plain,
% 1.73/1.94 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[572, 6603])).
% 1.73/1.94 tff(6605,plain,
% 1.73/1.94 (~r(s(elem!1), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4959, 106, 6604])).
% 1.73/1.94 tff(6606,plain,
% 1.73/1.94 (b(s(elem!1), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1039, 6605])).
% 1.73/1.94 tff(6607,plain,
% 1.73/1.94 (b(s(z), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[440, 625, 5466])).
% 1.73/1.94 tff(6608,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[5746, 619, 5466, 355, 131, 199, 106])).
% 1.73/1.94 tff(6609,plain,
% 1.73/1.94 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[420, 6608, 164])).
% 1.73/1.94 tff(6610,plain,
% 1.73/1.94 (b(elem!1, s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[428, 6609, 402])).
% 1.73/1.94 tff(6611,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6612,plain,
% 1.73/1.94 (((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(6613,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[6612])).
% 1.73/1.94 tff(6614,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.73/1.94 inference(transitivity,[status(thm)],[6613, 6611])).
% 1.73/1.94 tff(6615,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(6616,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[6615, 6614])).
% 1.73/1.94 tff(6617,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6616, 245, 4105, 6610, 355, 6607, 6606])).
% 1.73/1.94 tff(6618,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(6619,plain,
% 1.73/1.94 (~b(s(z), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6618, 619, 4105, 164, 131, 199, 106, 572])).
% 1.73/1.94 tff(6620,plain,
% 1.73/1.94 (r(s(z), z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[232, 6619])).
% 1.73/1.94 tff(6621,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[384, 141, 131, 6620, 619])).
% 1.73/1.94 tff(6622,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(6623,plain,
% 1.73/1.94 (~r(s(z), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[6622, 6602, 4105, 164, 199, 6598, 572])).
% 1.73/1.94 tff(6624,plain,
% 1.73/1.94 (b(s(z), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[389, 6623, 342])).
% 1.73/1.94 tff(6625,plain,
% 1.73/1.94 (~(elem!1 = s(elem!1))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1074, 1426])).
% 1.73/1.94 tff(6626,plain,
% 1.73/1.94 (~r(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3608, 2069, 131])).
% 1.73/1.94 tff(6627,plain,
% 1.73/1.94 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1724, 6626, 3600])).
% 1.73/1.94 tff(6628,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6629,plain,
% 1.73/1.95 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6630,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6629])).
% 1.73/1.95 tff(6631,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[6630, 6628])).
% 1.73/1.95 tff(6632,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6633,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6632, 6631])).
% 1.73/1.95 tff(6634,plain,
% 1.73/1.95 (~b(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6633, 245, 4105, 626, 5316, 2101, 288])).
% 1.73/1.95 tff(6635,plain,
% 1.73/1.95 (r(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[232, 6634])).
% 1.73/1.95 tff(6636,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[384, 141, 131, 6635, 619])).
% 1.73/1.95 tff(6637,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(6638,plain,
% 1.73/1.95 (~r(s(z), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6637, 170, 4105, 2101, 6606, 5466, 131, 572])).
% 1.73/1.95 tff(6639,plain,
% 1.73/1.95 (b(s(z), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[389, 6638, 342])).
% 1.73/1.95 tff(6640,plain,
% 1.73/1.95 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.73/1.95 inference(monotonicity,[status(thm)],[598, 199])).
% 1.73/1.95 tff(6641,plain,
% 1.73/1.95 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(symmetry,[status(thm)],[6640])).
% 1.73/1.95 tff(6642,plain,
% 1.73/1.95 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[170, 6641])).
% 1.73/1.95 tff(6643,plain,
% 1.73/1.95 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4922, 141, 572, 170])).
% 1.73/1.95 tff(6644,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.73/1.95 tff(6645,plain,
% 1.73/1.95 (b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[353, 11, 6644])).
% 1.73/1.95 tff(6646,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.95 tff(6647,plain,
% 1.73/1.95 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[422])).
% 1.73/1.95 tff(6648,plain,
% 1.73/1.95 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.73/1.95 inference(symmetry,[status(thm)],[6647])).
% 1.73/1.95 tff(6649,plain,
% 1.73/1.95 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6647])).
% 1.73/1.95 tff(6650,plain,
% 1.73/1.95 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6649])).
% 1.73/1.95 tff(6651,plain,
% 1.73/1.95 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 1.73/1.95 inference(symmetry,[status(thm)],[6650])).
% 1.73/1.95 tff(6652,plain,
% 1.73/1.95 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6651, 6648])).
% 1.73/1.95 tff(6653,plain,
% 1.73/1.95 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(symmetry,[status(thm)],[6652])).
% 1.73/1.95 tff(6654,plain,
% 1.73/1.95 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[1287, 6653])).
% 1.73/1.95 tff(6655,plain,
% 1.73/1.95 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(elem!1), z)),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6648])).
% 1.73/1.95 tff(6656,plain,
% 1.73/1.95 (r(s(elem!1), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.95 inference(symmetry,[status(thm)],[6655])).
% 1.73/1.95 tff(6657,plain,
% 1.73/1.95 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(elem!1))))), z))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6656])).
% 1.73/1.95 tff(6658,plain,
% 1.73/1.95 (r(elem!1, z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.73/1.95 inference(monotonicity,[status(thm)],[422])).
% 1.73/1.95 tff(6659,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), z) <=> r(elem!1, z)),
% 1.73/1.95 inference(symmetry,[status(thm)],[6658])).
% 1.73/1.95 tff(6660,plain,
% 1.73/1.95 (r(elem!1, z)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[106, 6659])).
% 1.73/1.95 tff(6661,plain,
% 1.73/1.95 (~r(s(elem!1), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1082, 6660, 1367])).
% 1.73/1.95 tff(6662,plain,
% 1.73/1.95 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6661, 6657])).
% 1.73/1.95 tff(6663,plain,
% 1.73/1.95 (((~![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))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6664,plain,
% 1.73/1.95 ((~![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))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6665,plain,
% 1.73/1.95 ((~![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)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6664, 6663])).
% 1.73/1.95 tff(6666,plain,
% 1.73/1.95 (b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6665, 32, 463])).
% 1.73/1.95 tff(6667,plain,
% 1.73/1.95 (b(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6666, 6662])).
% 1.73/1.95 tff(6668,plain,
% 1.73/1.95 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6647])).
% 1.73/1.95 tff(6669,plain,
% 1.73/1.95 (~r(z, s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4639, 6660, 1367])).
% 1.73/1.95 tff(6670,plain,
% 1.73/1.95 (b(z, s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[644, 6669])).
% 1.73/1.95 tff(6671,plain,
% 1.73/1.95 (b(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6670, 6668])).
% 1.73/1.95 tff(6672,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6673,plain,
% 1.73/1.95 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6674,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6673])).
% 1.73/1.95 tff(6675,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[6674, 6672])).
% 1.73/1.95 tff(6676,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6677,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6676, 6675])).
% 1.73/1.95 tff(6678,plain,
% 1.73/1.95 ((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6677, 245, 6671, 6667])).
% 1.73/1.95 tff(6679,plain,
% 1.73/1.95 (~b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6678, 6654])).
% 1.73/1.95 tff(6680,plain,
% 1.73/1.95 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(elem!1))))))) = z))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6681,plain,
% 1.73/1.95 (~(s(s(s(s(s(s(s(elem!1))))))) = z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6680, 20])).
% 1.73/1.95 tff(6682,plain,
% 1.73/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6683,plain,
% 1.73/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6684,plain,
% 1.73/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6683, 6682])).
% 1.73/1.95 tff(6685,plain,
% 1.73/1.95 (r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6684, 32, 6681, 6679])).
% 1.73/1.95 tff(6686,plain,
% 1.73/1.95 (((~![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(s(s(s(elem!1))))))), z)) | (~r(s(s(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)))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6687,plain,
% 1.73/1.95 ((~![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(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6688,plain,
% 1.73/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6687, 6686])).
% 1.73/1.95 tff(6689,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6688, 141, 106, 6646, 6685])).
% 1.73/1.95 tff(6690,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(6691,plain,
% 1.73/1.95 (~r(elem!1, s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6690, 6645, 422, 106, 6646])).
% 1.73/1.95 tff(6692,plain,
% 1.73/1.95 (b(elem!1, s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2777, 6691, 2774])).
% 1.73/1.95 tff(6693,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6694,plain,
% 1.73/1.95 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6695,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6694])).
% 1.73/1.95 tff(6696,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[6695, 6693])).
% 1.73/1.95 tff(6697,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6698,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6697, 6696])).
% 1.73/1.95 tff(6699,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6698, 245, 1287, 2939, 1103, 2101])).
% 1.73/1.95 tff(6700,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(6701,plain,
% 1.73/1.95 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6700, 6692, 2101, 6645])).
% 1.73/1.95 tff(6702,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.95 tff(6703,plain,
% 1.73/1.95 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2091, 32, 6702])).
% 1.73/1.95 tff(6704,plain,
% 1.73/1.95 (s(elem!1) = s(s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6703, 6701])).
% 1.73/1.95 tff(6705,plain,
% 1.73/1.95 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6704, 1939])).
% 1.73/1.95 tff(6706,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[11, 6705])).
% 1.73/1.95 tff(6707,plain,((s(s(s(elem!1))) = s(elem!1)) | r(s(elem!1), s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(6708,plain,
% 1.73/1.95 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6707, 6643, 2101, 2774, 402, 106, 6642, 6501])).
% 1.73/1.95 tff(6709,plain,
% 1.73/1.95 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6708])).
% 1.73/1.95 tff(6710,plain,
% 1.73/1.95 (b(elem!1, s(elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[2101, 6709])).
% 1.73/1.95 tff(6711,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6712,plain,
% 1.73/1.95 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6713,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6712])).
% 1.73/1.95 tff(6714,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[6713, 6711])).
% 1.73/1.95 tff(6715,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6716,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6715, 6714])).
% 1.73/1.95 tff(6717,plain,
% 1.73/1.95 (~b(s(z), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6716, 245, 4105, 6710, 6639, 6606])).
% 1.73/1.95 tff(6718,plain,
% 1.73/1.95 (r(s(z), s(elem!1))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[440, 6717, 5466])).
% 1.73/1.95 tff(6719,plain,
% 1.73/1.95 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6708])).
% 1.73/1.95 tff(6720,plain,
% 1.73/1.95 (r(z, s(elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[2069, 6719])).
% 1.73/1.95 tff(6721,plain,
% 1.73/1.95 (((~![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), s(elem!1))) | (~r(s(z), z)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6722,plain,
% 1.73/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6723,plain,
% 1.73/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6722, 6721])).
% 1.73/1.95 tff(6724,plain,
% 1.73/1.95 (~r(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6723, 141, 6720, 6718])).
% 1.73/1.95 tff(6725,plain,
% 1.73/1.95 (b(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[232, 6724])).
% 1.73/1.95 tff(6726,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6727,plain,
% 1.73/1.95 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(6728,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6727])).
% 1.73/1.95 tff(6729,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[6728, 6726])).
% 1.73/1.95 tff(6730,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(6731,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6730, 6729])).
% 1.73/1.95 tff(6732,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6731, 245, 4105, 6710, 6725, 6639, 6606])).
% 1.73/1.95 tff(6733,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(6734,plain,
% 1.73/1.95 (~r(s(s(s(elem!1))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6733, 6627, 4105, 2069, 6625, 106, 131, 572, 199])).
% 1.73/1.95 tff(6735,plain,
% 1.73/1.95 (b(s(s(s(elem!1))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[110, 6734, 102])).
% 1.73/1.95 tff(6736,plain,
% 1.73/1.95 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[199])).
% 1.73/1.95 tff(6737,plain,
% 1.73/1.95 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(symmetry,[status(thm)],[6736])).
% 1.73/1.95 tff(6738,plain,
% 1.73/1.95 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[6737])).
% 1.73/1.95 tff(6739,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[6626, 6738])).
% 1.73/1.95 tff(6740,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1320, 6739, 1487])).
% 1.73/1.95 tff(6741,plain,
% 1.73/1.95 (~b(s(s(s(elem!1))), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4172, 245, 4105, 6735, 6627])).
% 1.73/1.95 tff(6742,plain,
% 1.73/1.95 (r(s(s(s(elem!1))), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[37, 6741])).
% 1.73/1.95 tff(6743,plain,
% 1.73/1.95 (~r(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4183, 6742, 6627, 6740, 6735, 106])).
% 1.73/1.95 tff(6744,plain,
% 1.73/1.95 (b(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[232, 6743])).
% 1.73/1.95 tff(6745,plain,
% 1.73/1.95 (~r(s(z), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[6618, 6744, 4105, 164, 131, 199, 106, 572])).
% 1.73/1.95 tff(6746,plain,
% 1.73/1.95 (b(s(z), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[389, 6745, 342])).
% 1.73/1.95 tff(6747,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6748,plain,
% 1.73/1.96 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6749,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6748])).
% 1.73/1.96 tff(6750,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[6749, 6747])).
% 1.73/1.96 tff(6751,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(6752,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6751, 6750])).
% 1.73/1.96 tff(6753,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6752, 245, 4105, 6735, 6744, 6746, 6627])).
% 1.73/1.96 tff(6754,plain,((~r(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~r(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6755,plain,
% 1.73/1.96 (~r(z, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6754, 6602, 164, 4105, 199, 6598, 572, 102, 1487])).
% 1.73/1.96 tff(6756,plain,
% 1.73/1.96 (b(z, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[197, 6755])).
% 1.73/1.96 tff(6757,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6758,plain,
% 1.73/1.96 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6759,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6758])).
% 1.73/1.96 tff(6760,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[6759, 6757])).
% 1.73/1.96 tff(6761,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(6762,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6761, 6760])).
% 1.73/1.96 tff(6763,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6762, 245, 4105, 301, 1427, 235, 447])).
% 1.73/1.96 tff(6764,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6765,plain,
% 1.73/1.96 (~b(elem!1, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6764, 1427, 447, 235, 4105])).
% 1.73/1.96 tff(6766,plain,
% 1.73/1.96 (r(elem!1, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[281, 6765, 3599])).
% 1.73/1.96 tff(6767,plain,
% 1.73/1.96 (r(s(s(s(s(elem!1)))), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4612, 6766, 422])).
% 1.73/1.96 tff(6768,plain,
% 1.73/1.96 (~r(z, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4226, 6767, 106])).
% 1.73/1.96 tff(6769,plain,
% 1.73/1.96 (b(z, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1421, 6768])).
% 1.73/1.96 tff(6770,plain,
% 1.73/1.96 (~r(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4206, 6766, 572])).
% 1.73/1.96 tff(6771,plain,
% 1.73/1.96 (b(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[369, 6770, 358])).
% 1.73/1.96 tff(6772,plain,
% 1.73/1.96 (~r(s(z), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[225, 6767, 106])).
% 1.73/1.96 tff(6773,plain,
% 1.73/1.96 (b(s(z), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[232, 6772])).
% 1.73/1.96 tff(6774,plain,
% 1.73/1.96 (~b(z, s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4196, 6769, 4105, 6771, 6773])).
% 1.73/1.96 tff(6775,plain,
% 1.73/1.96 (r(z, s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[644, 6774])).
% 1.73/1.96 tff(6776,plain,
% 1.73/1.96 (~r(elem!1, s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4639, 6775, 131])).
% 1.73/1.96 tff(6777,plain,
% 1.73/1.96 (b(elem!1, s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2777, 6776, 2774])).
% 1.73/1.96 tff(6778,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6779,plain,
% 1.73/1.96 (((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6780,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~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(X0, 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(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6779])).
% 1.73/1.96 tff(6781,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~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(X0, 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(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[6780, 6778])).
% 1.73/1.96 tff(6782,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(6783,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6782, 6781])).
% 1.73/1.96 tff(6784,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6783, 245, 4105, 1427, 6777, 235, 6771, 6769])).
% 1.73/1.96 tff(6785,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(z)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6786,plain,
% 1.73/1.96 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6785, 6756, 4105, 6625, 6602, 6598, 6597, 402, 572, 210, 6624])).
% 1.73/1.96 tff(6787,plain,
% 1.73/1.96 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[110, 6786, 102])).
% 1.73/1.96 tff(6788,plain,
% 1.73/1.96 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[577, 6787, 572])).
% 1.73/1.96 tff(6789,plain,
% 1.73/1.96 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4922, 141, 572, 6787])).
% 1.73/1.96 tff(6790,plain,
% 1.73/1.96 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6787, 6641])).
% 1.73/1.96 tff(6791,plain,
% 1.73/1.96 (~r(s(elem!1), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4959, 6598, 6604])).
% 1.73/1.96 tff(6792,plain,
% 1.73/1.96 (~r(elem!1, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4128, 1355, 131])).
% 1.73/1.96 tff(6793,plain,
% 1.73/1.96 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1724, 6792, 1717])).
% 1.73/1.96 tff(6794,plain,
% 1.73/1.96 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6707, 6793, 6646, 2774, 422, 106, 6702, 6644])).
% 1.73/1.96 tff(6795,plain,
% 1.73/1.96 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6794])).
% 1.73/1.96 tff(6796,plain,
% 1.73/1.96 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 1.73/1.96 inference(symmetry,[status(thm)],[6795])).
% 1.73/1.96 tff(6797,plain,
% 1.73/1.96 ((~r(s(elem!1), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6796])).
% 1.73/1.96 tff(6798,plain,
% 1.73/1.96 (~r(s(s(s(elem!1))), z)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[1037, 6797])).
% 1.73/1.96 tff(6799,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1355, 6798])).
% 1.73/1.96 tff(6800,plain,((~r(s(s(s(elem!1))), z)) | r(s(elem!1), z) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (elem!1 = s(elem!1)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | r(s(elem!1), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6801,plain,
% 1.73/1.96 (~r(s(s(s(elem!1))), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6800, 6791, 6790, 6625, 402, 6598, 6789, 6788, 3600, 6602])).
% 1.73/1.96 tff(6802,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[37, 6801])).
% 1.73/1.96 tff(6803,plain,
% 1.73/1.96 (b(s(elem!1), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1039, 6791])).
% 1.73/1.96 tff(6804,plain,
% 1.73/1.96 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[299, 245, 6756, 6802, 6803])).
% 1.73/1.96 tff(6805,plain,
% 1.73/1.96 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[353, 6804, 6788])).
% 1.73/1.96 tff(6806,plain,
% 1.73/1.96 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[594, 6805, 199, 5466])).
% 1.73/1.96 tff(6807,plain,
% 1.73/1.96 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[612, 6805, 199, 6806])).
% 1.73/1.96 tff(6808,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1161, 141, 131, 2628, 722])).
% 1.73/1.96 tff(6809,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6810,plain,
% 1.73/1.96 (~r(s(s(s(s(s(z))))), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6809, 2628, 131])).
% 1.73/1.96 tff(6811,plain,
% 1.73/1.96 (b(s(s(s(s(s(z))))), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[738, 6810])).
% 1.73/1.96 tff(6812,plain,
% 1.73/1.96 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1179, 245, 235, 234, 6811])).
% 1.73/1.96 tff(6813,plain,
% 1.73/1.96 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6812, 6384])).
% 1.73/1.96 tff(6814,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[797, 6512, 6813, 673])).
% 1.73/1.96 tff(6815,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6816,plain,
% 1.73/1.96 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6815, 6807, 199, 6787, 6756, 6802, 6602])).
% 1.73/1.96 tff(6817,plain,
% 1.73/1.96 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[787, 6816, 5814])).
% 1.73/1.96 tff(6818,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6819,plain,
% 1.73/1.96 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6820,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6819])).
% 1.73/1.96 tff(6821,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[6820, 6818])).
% 1.73/1.96 tff(6822,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(6823,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6822, 6821])).
% 1.73/1.96 tff(6824,plain,
% 1.73/1.96 (~b(z, s(s(s(s(s(z))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6823, 245, 4105, 301, 447, 4878])).
% 1.73/1.96 tff(6825,plain,
% 1.73/1.96 (r(z, s(s(s(s(s(z))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[758, 6824])).
% 1.73/1.96 tff(6826,plain,
% 1.73/1.96 (~b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5864, 245, 301, 447, 4878])).
% 1.73/1.96 tff(6827,plain,
% 1.73/1.96 (r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1698, 6826])).
% 1.73/1.96 tff(6828,plain,
% 1.73/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(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(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6829,plain,
% 1.73/1.96 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6830,plain,
% 1.73/1.96 (((~![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(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6829])).
% 1.73/1.96 tff(6831,plain,
% 1.73/1.96 (((~![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(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[6830, 6828])).
% 1.73/1.96 tff(6832,plain,
% 1.73/1.96 ((~![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))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(6833,plain,
% 1.73/1.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6832, 6831])).
% 1.73/1.96 tff(6834,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6833, 141, 4669, 6827, 6825])).
% 1.73/1.96 tff(6835,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6836,plain,
% 1.73/1.96 (~b(elem!1, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6835, 6817, 6624, 4105])).
% 1.73/1.96 tff(6837,plain,
% 1.73/1.96 (r(elem!1, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[281, 6836, 210])).
% 1.73/1.96 tff(6838,plain,
% 1.73/1.96 (~r(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4206, 6837, 572])).
% 1.73/1.96 tff(6839,plain,
% 1.73/1.96 (b(s(elem!1), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[369, 6838, 6597])).
% 1.73/1.96 tff(6840,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6841,plain,
% 1.73/1.96 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6842,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6841])).
% 1.73/1.96 tff(6843,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[6842, 6840])).
% 1.73/1.96 tff(6844,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(6845,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6844, 6843])).
% 1.73/1.96 tff(6846,plain,
% 1.73/1.96 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6845, 245, 6756, 6802, 6803])).
% 1.73/1.96 tff(6847,plain,
% 1.73/1.96 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2091, 32, 6789])).
% 1.73/1.96 tff(6848,plain,
% 1.73/1.96 (s(elem!1) = s(s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6847, 6846])).
% 1.73/1.96 tff(6849,plain,
% 1.73/1.96 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.96 inference(symmetry,[status(thm)],[6848])).
% 1.73/1.96 tff(6850,plain,
% 1.73/1.96 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6849])).
% 1.73/1.96 tff(6851,plain,
% 1.73/1.96 (b(z, s(elem!1))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6756, 6850])).
% 1.73/1.96 tff(6852,plain,
% 1.73/1.96 (r(s(s(s(s(elem!1)))), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4612, 6837, 402])).
% 1.73/1.96 tff(6853,plain,
% 1.73/1.96 (~r(z, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4226, 6852, 6598])).
% 1.73/1.96 tff(6854,plain,
% 1.73/1.96 (b(z, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1421, 6853])).
% 1.73/1.96 tff(6855,plain,
% 1.73/1.96 (~r(s(z), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[225, 6852, 6598])).
% 1.73/1.96 tff(6856,plain,
% 1.73/1.96 (b(s(z), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[232, 6855])).
% 1.73/1.96 tff(6857,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4196, 6856, 6854, 4105, 6851, 6839])).
% 1.73/1.96 tff(6858,plain,(b(elem!1, z) | (~b(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6859,plain,
% 1.73/1.96 (b(elem!1, z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6858, 6596, 1277, 5447, 96, 7, 1312])).
% 1.73/1.96 tff(6860,plain,
% 1.73/1.96 (r(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[614])).
% 1.73/1.96 tff(6861,plain,
% 1.73/1.96 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/1.96 inference(symmetry,[status(thm)],[6860])).
% 1.73/1.96 tff(6862,plain,
% 1.73/1.96 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[599, 598])).
% 1.73/1.96 tff(6863,plain,
% 1.73/1.96 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6862])).
% 1.73/1.96 tff(6864,plain,
% 1.73/1.96 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.73/1.96 inference(transitivity,[status(thm)],[604, 6863, 157])).
% 1.73/1.96 tff(6865,plain,
% 1.73/1.96 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6864])).
% 1.73/1.96 tff(6866,plain,
% 1.73/1.96 (s(s(s(z))) = s(elem!1)),
% 1.73/1.96 inference(transitivity,[status(thm)],[1043, 6865, 155])).
% 1.73/1.96 tff(6867,plain,
% 1.73/1.96 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6866])).
% 1.73/1.96 tff(6868,plain,
% 1.73/1.96 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[586, 6867, 49, 580])).
% 1.73/1.96 tff(6869,plain,
% 1.73/1.96 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6868])).
% 1.73/1.96 tff(6870,plain,
% 1.73/1.96 (s(z) = s(s(s(elem!1)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[591, 6869, 113])).
% 1.73/1.96 tff(6871,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1128, 6870])).
% 1.73/1.96 tff(6872,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(6873,plain,
% 1.73/1.96 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[6872, 199])).
% 1.73/1.96 tff(6874,plain,
% 1.73/1.96 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[6873, 5915])).
% 1.73/1.96 tff(6875,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[614])).
% 1.73/1.96 tff(6876,plain,
% 1.73/1.96 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[6875])).
% 1.73/1.96 tff(6877,plain,
% 1.73/1.96 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1065, 5466, 199])).
% 1.73/1.96 tff(6878,plain,
% 1.73/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6879,plain,
% 1.73/1.96 (((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(6880,plain,
% 1.73/1.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[6879])).
% 1.73/1.97 tff(6881,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[6880, 6878])).
% 1.73/1.97 tff(6882,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6883,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6882, 6881])).
% 1.73/1.97 tff(6884,plain,
% 1.73/1.97 (~r(s(elem!1), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6883, 141, 572, 619])).
% 1.73/1.97 tff(6885,plain,
% 1.73/1.97 (b(s(elem!1), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[369, 6884, 6597])).
% 1.73/1.97 tff(6886,plain,
% 1.73/1.97 (((~![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(z))))), elem!1)) | (~r(s(elem!1), 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(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6887,plain,
% 1.73/1.97 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6888,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), 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(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[6887])).
% 1.73/1.97 tff(6889,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), 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(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[6888, 6886])).
% 1.73/1.97 tff(6890,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6891,plain,
% 1.73/1.97 ((~![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(z))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6890, 6889])).
% 1.73/1.97 tff(6892,plain,
% 1.73/1.97 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6891, 141, 572, 2628])).
% 1.73/1.97 tff(6893,plain,
% 1.73/1.97 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1156, 32, 1153, 6892])).
% 1.73/1.97 tff(6894,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6895,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6896,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6895, 6894])).
% 1.73/1.97 tff(6897,plain,
% 1.73/1.97 (~r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6896, 141, 619, 2628])).
% 1.73/1.97 tff(6898,plain,
% 1.73/1.97 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[809, 6897])).
% 1.73/1.97 tff(6899,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6900,plain,
% 1.73/1.97 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6901,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[6900])).
% 1.73/1.97 tff(6902,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[6901, 6899])).
% 1.73/1.97 tff(6903,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6904,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6903, 6902])).
% 1.73/1.97 tff(6905,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6904, 245, 655, 4188, 6898, 6893])).
% 1.73/1.97 tff(6906,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(6907,plain,
% 1.73/1.97 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6906, 6885, 619, 6877, 572, 6607])).
% 1.73/1.97 tff(6908,plain,
% 1.73/1.97 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[787, 6907, 5814])).
% 1.73/1.97 tff(6909,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6910,plain,
% 1.73/1.97 (((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6911,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[6910])).
% 1.73/1.97 tff(6912,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[6911, 6909])).
% 1.73/1.97 tff(6913,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6914,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6913, 6912])).
% 1.73/1.97 tff(6915,plain,
% 1.73/1.97 (~b(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6914, 245, 4105, 4186, 6908])).
% 1.73/1.97 tff(6916,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[738, 6915])).
% 1.73/1.97 tff(6917,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6918,plain,
% 1.73/1.97 (((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6919,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[6918])).
% 1.73/1.97 tff(6920,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[6919, 6917])).
% 1.73/1.97 tff(6921,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6922,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 1.73/1.97 tff(6923,plain,
% 1.73/1.97 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6922, 245, 4105, 4186, 1427, 4878])).
% 1.73/1.97 tff(6924,plain,
% 1.73/1.97 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6923, 6384])).
% 1.73/1.97 tff(6925,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[797, 6924, 6873])).
% 1.73/1.97 tff(6926,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6925, 6382])).
% 1.73/1.97 tff(6927,plain,
% 1.73/1.97 (~b(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6914, 245, 4105, 4186, 4878])).
% 1.73/1.97 tff(6928,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[738, 6927])).
% 1.73/1.97 tff(6929,plain,
% 1.73/1.97 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6930,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[6929])).
% 1.73/1.97 tff(6931,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[6930, 4517])).
% 1.73/1.97 tff(6932,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6933,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6932, 6931])).
% 1.73/1.97 tff(6934,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6933, 245, 4105, 4186, 1427])).
% 1.73/1.97 tff(6935,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[37, 6934])).
% 1.73/1.97 tff(6936,plain,
% 1.73/1.97 (((~![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(s(z))))), z)) | (~r(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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6937,plain,
% 1.73/1.97 ((~![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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6938,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6937, 6936])).
% 1.73/1.97 tff(6939,plain,
% 1.73/1.97 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6938, 141, 6935, 6928])).
% 1.73/1.97 tff(6940,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6939, 6926])).
% 1.73/1.97 tff(6941,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(6942,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6941, 6908, 4105, 4186, 199])).
% 1.73/1.97 tff(6943,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[110, 6942, 102])).
% 1.73/1.97 tff(6944,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6945,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6946,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6945, 6944])).
% 1.73/1.97 tff(6947,plain,
% 1.73/1.97 (~r(s(s(s(elem!1))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6946, 141, 619, 6943])).
% 1.73/1.97 tff(6948,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[265, 6947])).
% 1.73/1.97 tff(6949,plain,
% 1.73/1.97 (~r(s(z), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1143, 6943, 619])).
% 1.73/1.97 tff(6950,plain,
% 1.73/1.97 (b(s(z), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1133, 6949])).
% 1.73/1.97 tff(6951,plain,
% 1.73/1.97 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6906, 6607, 6885, 6877, 572, 619])).
% 1.73/1.97 tff(6952,plain,
% 1.73/1.97 (b(s(s(s(s(s(z))))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[787, 6951, 5814])).
% 1.73/1.97 tff(6953,plain,
% 1.73/1.97 (~b(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6914, 245, 4105, 4186, 6952])).
% 1.73/1.97 tff(6954,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[738, 6953])).
% 1.73/1.97 tff(6955,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 1.73/1.97 tff(6956,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6955, 6382])).
% 1.73/1.97 tff(6957,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6958,plain,
% 1.73/1.97 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(6959,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[6958])).
% 1.73/1.97 tff(6960,plain,
% 1.73/1.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[6959, 6957])).
% 1.73/1.97 tff(6961,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(6962,plain,
% 1.73/1.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6961, 6960])).
% 1.73/1.97 tff(6963,plain,
% 1.73/1.97 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6962, 141, 2069, 722])).
% 1.73/1.97 tff(6964,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6963, 6956])).
% 1.73/1.97 tff(6965,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(6966,plain,
% 1.73/1.97 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6965, 6954, 2069, 199])).
% 1.73/1.97 tff(6967,plain,
% 1.73/1.97 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[797, 6966, 6873])).
% 1.73/1.97 tff(6968,plain,
% 1.73/1.97 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[6967, 6506])).
% 1.73/1.97 tff(6969,plain,
% 1.73/1.97 (~b(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6941, 6952, 4105, 4186, 199])).
% 1.73/1.97 tff(6970,plain,
% 1.73/1.97 (r(s(s(s(elem!1))), elem!1)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[110, 6969, 102])).
% 1.73/1.97 tff(6971,plain,
% 1.73/1.97 (~r(s(s(s(elem!1))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[6946, 141, 619, 6970])).
% 1.73/1.97 tff(6972,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[265, 6971])).
% 1.73/1.97 tff(6973,plain,
% 1.73/1.97 (~r(s(z), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1143, 6970, 619])).
% 1.73/1.97 tff(6974,plain,
% 1.73/1.97 (b(s(z), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1133, 6973])).
% 1.73/1.98 tff(6975,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(6976,plain,
% 1.73/1.98 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(6977,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[6976])).
% 1.73/1.98 tff(6978,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[6977, 6975])).
% 1.73/1.98 tff(6979,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(6980,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[6979, 6978])).
% 1.73/1.98 tff(6981,plain,
% 1.73/1.98 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6980, 245, 6974, 6972])).
% 1.73/1.98 tff(6982,plain,
% 1.73/1.98 (~b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6981, 6968])).
% 1.73/1.98 tff(6983,plain,
% 1.73/1.98 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[809, 6982])).
% 1.73/1.98 tff(6984,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(6985,plain,
% 1.73/1.98 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(6986,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[6985])).
% 1.73/1.98 tff(6987,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[6986, 6984])).
% 1.73/1.98 tff(6988,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(6989,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[6988, 6987])).
% 1.73/1.98 tff(6990,plain,
% 1.73/1.98 (~b(z, s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6989, 245, 4105, 4186, 6952])).
% 1.73/1.98 tff(6991,plain,
% 1.73/1.98 (r(z, s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[758, 6990])).
% 1.73/1.98 tff(6992,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(6993,plain,
% 1.73/1.98 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(6994,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[6993])).
% 1.73/1.98 tff(6995,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[6994, 6992])).
% 1.73/1.98 tff(6996,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(6997,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[6996, 6995])).
% 1.73/1.98 tff(6998,plain,
% 1.73/1.98 ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6997, 245, 6974, 6972])).
% 1.73/1.98 tff(6999,plain,
% 1.73/1.98 (~b(s(z), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6998, 6968])).
% 1.73/1.98 tff(7000,plain,
% 1.73/1.98 (r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1698, 6999])).
% 1.73/1.98 tff(7001,plain,
% 1.73/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(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), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7002,plain,
% 1.73/1.98 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7003,plain,
% 1.73/1.98 (((~![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(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[7002])).
% 1.73/1.98 tff(7004,plain,
% 1.73/1.98 (((~![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(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[7003, 7001])).
% 1.73/1.98 tff(7005,plain,
% 1.73/1.98 ((~![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(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(7006,plain,
% 1.73/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[7005, 7004])).
% 1.73/1.98 tff(7007,plain,
% 1.73/1.98 (~r(s(z), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7006, 141, 7000, 6991])).
% 1.73/1.98 tff(7008,plain,
% 1.73/1.98 (b(s(z), z)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[232, 7007])).
% 1.73/1.98 tff(7009,plain,
% 1.73/1.98 (~b(elem!1, s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[4214, 245, 4105, 4186, 7008])).
% 1.73/1.98 tff(7010,plain,
% 1.73/1.98 (r(elem!1, s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[281, 7009, 210])).
% 1.73/1.98 tff(7011,plain,
% 1.73/1.98 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6045, 141, 7010, 6983])).
% 1.73/1.98 tff(7012,plain,
% 1.73/1.98 (b(elem!1, s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[720, 7011, 5783])).
% 1.73/1.98 tff(7013,plain,
% 1.73/1.98 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[577, 6970, 572])).
% 1.73/1.98 tff(7014,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7015,plain,
% 1.73/1.98 (((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7016,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[7015])).
% 1.73/1.98 tff(7017,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[7016, 7014])).
% 1.73/1.98 tff(7018,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(7019,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[7018, 7017])).
% 1.73/1.98 tff(7020,plain,
% 1.73/1.98 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7019, 245, 6607, 6885, 6972])).
% 1.73/1.98 tff(7021,plain,
% 1.73/1.98 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[353, 7020, 7013])).
% 1.73/1.98 tff(7022,plain,
% 1.73/1.98 (~(s(s(s(z))) = elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[870, 7021, 199])).
% 1.73/1.98 tff(7023,plain,
% 1.73/1.98 (~r(z, s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6833, 141, 7000, 6991])).
% 1.73/1.98 tff(7024,plain,
% 1.73/1.98 (b(z, s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1421, 7023])).
% 1.73/1.98 tff(7025,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)) | (~b(elem!1, s(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(X0, 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)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7026,plain,
% 1.73/1.98 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7027,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[7026])).
% 1.73/1.98 tff(7028,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[7027, 7025])).
% 1.73/1.98 tff(7029,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(7030,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[7029, 7028])).
% 1.73/1.98 tff(7031,plain,
% 1.73/1.98 (~b(s(s(s(z))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7030, 245, 4105, 4186, 5823, 911, 6123])).
% 1.73/1.98 tff(7032,plain,
% 1.73/1.98 (r(s(s(s(z))), elem!1)),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6065, 32, 7031, 6213])).
% 1.73/1.98 tff(7033,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7034,plain,
% 1.73/1.98 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7035,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[7034])).
% 1.73/1.98 tff(7036,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[7035, 7033])).
% 1.73/1.98 tff(7037,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(7038,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[7037, 7036])).
% 1.73/1.98 tff(7039,plain,
% 1.73/1.98 (~b(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7038, 245, 4105, 355, 5823, 911, 6123])).
% 1.73/1.98 tff(7040,plain,
% 1.73/1.98 (r(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[895, 32, 892, 7039])).
% 1.73/1.98 tff(7041,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6317, 141, 619, 7040, 7032])).
% 1.73/1.98 tff(7042,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(7043,plain,
% 1.73/1.98 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[7042, 911, 6213, 4105, 355, 5823, 619, 4186])).
% 1.73/1.98 tff(7044,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1515, 7043])).
% 1.73/1.98 tff(7045,plain,
% 1.73/1.98 (~r(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[6027, 141, 2641, 7044])).
% 1.73/1.98 tff(7046,plain,
% 1.73/1.98 (b(s(s(s(z))), s(z))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[895, 32, 7045, 892])).
% 1.73/1.98 tff(7047,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.73/1.98 tff(7048,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(7049,plain,
% 1.73/1.98 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7050,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[7049])).
% 1.73/1.99 tff(7051,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7050, 7048])).
% 1.73/1.99 tff(7052,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7053,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7052, 7051])).
% 1.73/1.99 tff(7054,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7053, 245, 3615, 7047, 4187, 911, 7046])).
% 1.73/1.99 tff(7055,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(7056,plain,
% 1.73/1.99 (~b(s(s(s(z))), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7055, 6974, 6972, 7024, 7000, 7022, 4105, 7008, 7012, 619, 4186])).
% 1.73/1.99 tff(7057,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.73/1.99 tff(7058,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.73/1.99 tff(7059,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[836, 32, 833, 7058, 7057])).
% 1.73/1.99 tff(7060,plain,(r(s(s(s(z))), z) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(7061,plain,
% 1.73/1.99 (r(s(s(s(z))), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7060, 7056])).
% 1.73/1.99 tff(7062,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7063,plain,
% 1.73/1.99 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7064,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[7063])).
% 1.73/1.99 tff(7065,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7064, 7062])).
% 1.73/1.99 tff(7066,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7067,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7066, 7065])).
% 1.73/1.99 tff(7068,plain,
% 1.73/1.99 (~b(s(s(s(elem!1))), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7067, 245, 7008, 6972, 7024])).
% 1.73/1.99 tff(7069,plain,
% 1.73/1.99 (r(s(s(s(elem!1))), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[37, 7068])).
% 1.73/1.99 tff(7070,plain,
% 1.73/1.99 (((~![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(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7071,plain,
% 1.73/1.99 (((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7072,plain,
% 1.73/1.99 (((~![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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[7071])).
% 1.73/1.99 tff(7073,plain,
% 1.73/1.99 (((~![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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7072, 7070])).
% 1.73/1.99 tff(7074,plain,
% 1.73/1.99 ((~![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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7075,plain,
% 1.73/1.99 ((~![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(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7074, 7073])).
% 1.73/1.99 tff(7076,plain,
% 1.73/1.99 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7075, 141, 7069, 7061])).
% 1.73/1.99 tff(7077,plain,
% 1.73/1.99 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(symmetry,[status(thm)],[6875])).
% 1.73/1.99 tff(7078,plain,
% 1.73/1.99 ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[6860])).
% 1.73/1.99 tff(7079,plain,
% 1.73/1.99 (((~![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(s(z))))), z)) | (~r(s(s(s(elem!1))), 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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7080,plain,
% 1.73/1.99 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7081,plain,
% 1.73/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), 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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[7080])).
% 1.73/1.99 tff(7082,plain,
% 1.73/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), 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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7081, 7079])).
% 1.73/1.99 tff(7083,plain,
% 1.73/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7084,plain,
% 1.73/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7083, 7082])).
% 1.73/1.99 tff(7085,plain,
% 1.73/1.99 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7084, 141, 7069, 6954])).
% 1.73/1.99 tff(7086,plain,
% 1.73/1.99 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7085, 7078])).
% 1.73/1.99 tff(7087,plain,
% 1.73/1.99 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6009, 7086, 6874])).
% 1.73/1.99 tff(7088,plain,
% 1.73/1.99 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7087, 7077])).
% 1.73/1.99 tff(7089,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[6339, 141, 6013, 740, 979])).
% 1.73/1.99 tff(7090,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(7091,plain,
% 1.73/1.99 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7090, 7061, 6991])).
% 1.73/1.99 tff(7092,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1515, 7091])).
% 1.73/1.99 tff(7093,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7094,plain,
% 1.73/1.99 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7095,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[7094])).
% 1.73/1.99 tff(7096,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7095, 7093])).
% 1.73/1.99 tff(7097,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7098,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7097, 7096])).
% 1.73/1.99 tff(7099,plain,
% 1.73/1.99 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7098, 245, 7012, 6952, 7092])).
% 1.73/1.99 tff(7100,plain,
% 1.73/1.99 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7099, 7088])).
% 1.73/1.99 tff(7101,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7102,plain,
% 1.73/1.99 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7103,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[7102])).
% 1.73/1.99 tff(7104,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7103, 7101])).
% 1.73/1.99 tff(7105,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7106,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7105, 7104])).
% 1.73/1.99 tff(7107,plain,
% 1.73/1.99 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7106, 245, 6607, 6885, 6972])).
% 1.73/1.99 tff(7108,plain,
% 1.73/1.99 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4922, 141, 572, 6970])).
% 1.73/1.99 tff(7109,plain,
% 1.73/1.99 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2091, 32, 7108])).
% 1.73/1.99 tff(7110,plain,
% 1.73/1.99 (s(elem!1) = s(s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7109, 7107])).
% 1.73/1.99 tff(7111,plain,
% 1.73/1.99 (~(s(elem!1) = s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[594, 7021, 199, 5466])).
% 1.73/1.99 tff(7112,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.73/1.99 tff(7113,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.73/1.99 tff(7114,plain,
% 1.73/1.99 (s(elem!1) = s(s(s(z)))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7113, 7112])).
% 1.73/1.99 tff(7115,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[610, 7114])).
% 1.73/1.99 tff(7116,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(7117,plain,
% 1.73/1.99 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7116, 7111, 7110])).
% 1.73/1.99 tff(7118,plain,
% 1.73/1.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7119,plain,
% 1.73/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7120,plain,
% 1.73/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7119, 7118])).
% 1.73/1.99 tff(7121,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7120, 32, 7117, 7100, 7076])).
% 1.73/1.99 tff(7122,plain,((~r(s(z), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(7123,plain,
% 1.73/1.99 (~r(z, s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7122, 619, 4105, 4186, 199, 572, 102])).
% 1.73/1.99 tff(7124,plain,
% 1.73/1.99 (b(z, s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[197, 7123])).
% 1.73/1.99 tff(7125,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7126,plain,
% 1.73/1.99 (((~b(s(z), s(elem!1))) | (~b(s(z), s(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), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7127,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[7126])).
% 1.73/1.99 tff(7128,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[7127, 7125])).
% 1.73/1.99 tff(7129,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7130,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[7129, 7128])).
% 1.73/1.99 tff(7131,plain,
% 1.73/1.99 (~b(s(z), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[7130, 245, 7124, 6607, 6950, 6948])).
% 1.73/1.99 tff(7132,plain,
% 1.73/1.99 (r(s(z), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[232, 7131])).
% 1.73/1.99 tff(7133,plain,
% 1.73/1.99 (((~![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))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(7134,plain,
% 1.73/1.99 ((~![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))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(7135,plain,
% 1.73/1.99 ((~![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)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7134, 7133])).
% 1.73/2.00 tff(7136,plain,
% 1.73/2.00 (~r(s(s(s(s(s(z))))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7135, 141, 7132, 6916])).
% 1.73/2.00 tff(7137,plain,
% 1.73/2.00 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[809, 7136])).
% 1.73/2.00 tff(7138,plain,
% 1.73/2.00 (~r(s(z), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5856, 141, 7132, 6916])).
% 1.73/2.00 tff(7139,plain,
% 1.73/2.00 (b(s(z), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1698, 7138])).
% 1.73/2.00 tff(7140,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7141,plain,
% 1.73/2.00 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7142,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7141])).
% 1.73/2.00 tff(7143,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[7142, 7140])).
% 1.73/2.00 tff(7144,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(7145,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7144, 7143])).
% 1.73/2.00 tff(7146,plain,
% 1.73/2.00 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7145, 245, 6948, 7139, 7137])).
% 1.73/2.00 tff(7147,plain,
% 1.73/2.00 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7146, 6876])).
% 1.73/2.00 tff(7148,plain,
% 1.73/2.00 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6009, 7147, 6874])).
% 1.73/2.00 tff(7149,plain,
% 1.73/2.00 (r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7148, 6861])).
% 1.73/2.00 tff(7150,plain,
% 1.73/2.00 (~(s(s(s(z))) = elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5452, 199])).
% 1.73/2.00 tff(7151,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7152,plain,
% 1.73/2.00 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7153,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7152])).
% 1.73/2.00 tff(7154,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[7153, 7151])).
% 1.73/2.00 tff(7155,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(7156,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 1.73/2.00 tff(7157,plain,
% 1.73/2.00 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7156, 245, 6948, 7139, 6908, 7137])).
% 1.73/2.00 tff(7158,plain,
% 1.73/2.00 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7157, 6384])).
% 1.73/2.00 tff(7159,plain,
% 1.73/2.00 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[797, 7158, 6873])).
% 1.73/2.00 tff(7160,plain,
% 1.73/2.00 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7159, 6382])).
% 1.73/2.00 tff(7161,plain,
% 1.73/2.00 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7106, 245, 6607, 6885, 6948])).
% 1.73/2.00 tff(7162,plain,
% 1.73/2.00 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4922, 141, 572, 6943])).
% 1.73/2.00 tff(7163,plain,
% 1.73/2.00 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2091, 32, 7162])).
% 1.73/2.00 tff(7164,plain,
% 1.73/2.00 (s(elem!1) = s(s(s(elem!1)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7163, 7161])).
% 1.73/2.00 tff(7165,plain,
% 1.73/2.00 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/2.00 inference(symmetry,[status(thm)],[7164])).
% 1.73/2.00 tff(7166,plain,
% 1.73/2.00 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7165])).
% 1.73/2.00 tff(7167,plain,
% 1.73/2.00 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 1.73/2.00 inference(symmetry,[status(thm)],[7166])).
% 1.73/2.00 tff(7168,plain,
% 1.73/2.00 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7165])).
% 1.73/2.00 tff(7169,plain,
% 1.73/2.00 (b(z, s(elem!1))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7124, 7168])).
% 1.73/2.00 tff(7170,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7171,plain,
% 1.73/2.00 (((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7172,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7171])).
% 1.73/2.00 tff(7173,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[7172, 7170])).
% 1.73/2.00 tff(7174,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(7175,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7174, 7173])).
% 1.73/2.00 tff(7176,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7175, 245, 4105, 1103, 655, 4188, 838])).
% 1.73/2.00 tff(7177,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(7178,plain,
% 1.73/2.00 (~b(elem!1, s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7177, 7169, 6607, 6885, 4105])).
% 1.73/2.00 tff(7179,plain,
% 1.73/2.00 (r(elem!1, s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2777, 7178, 6625])).
% 1.73/2.00 tff(7180,plain,
% 1.73/2.00 (r(elem!1, s(s(s(elem!1))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7179, 7167])).
% 1.73/2.00 tff(7181,plain,
% 1.73/2.00 (((~![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(z))))))) | (~r(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(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7182,plain,
% 1.73/2.00 (((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7183,plain,
% 1.73/2.00 (((~![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(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7182])).
% 1.73/2.00 tff(7184,plain,
% 1.73/2.00 (((~![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(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[7183, 7181])).
% 1.73/2.00 tff(7185,plain,
% 1.73/2.00 ((~![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(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(7186,plain,
% 1.73/2.00 ((~![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(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7185, 7184])).
% 1.73/2.00 tff(7187,plain,
% 1.73/2.00 ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7186, 141, 7180])).
% 1.73/2.00 tff(7188,plain,
% 1.73/2.00 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7187, 7160])).
% 1.73/2.00 tff(7189,plain,
% 1.73/2.00 (b(elem!1, s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[720, 7188, 5783])).
% 1.73/2.00 tff(7190,plain,
% 1.73/2.00 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6319, 7189, 619, 6908, 7150, 7139])).
% 1.73/2.00 tff(7191,plain,
% 1.73/2.00 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1515, 7190])).
% 1.73/2.00 tff(7192,plain,
% 1.73/2.00 (((~![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(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7193,plain,
% 1.73/2.00 ((~![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(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(7194,plain,
% 1.73/2.00 ((~![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(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7193, 7192])).
% 1.73/2.00 tff(7195,plain,
% 1.73/2.00 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7194, 141, 7191, 7149])).
% 1.73/2.00 tff(7196,plain,
% 1.73/2.00 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[577, 6943, 572])).
% 1.73/2.00 tff(7197,plain,
% 1.73/2.00 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7019, 245, 6607, 6885, 6948])).
% 1.73/2.00 tff(7198,plain,
% 1.73/2.00 (s(s(s(elem!1))) = s(elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[353, 7197, 7196])).
% 1.73/2.00 tff(7199,plain,
% 1.73/2.00 (~(s(elem!1) = s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[594, 7198, 199, 5466])).
% 1.73/2.00 tff(7200,plain,
% 1.73/2.00 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7116, 7199, 7164])).
% 1.73/2.00 tff(7201,plain,
% 1.73/2.00 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7120, 32, 7200, 7195])).
% 1.73/2.00 tff(7202,plain,
% 1.73/2.00 (~b(z, s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6989, 245, 4105, 4186, 6908])).
% 1.73/2.00 tff(7203,plain,
% 1.73/2.00 (r(z, s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[758, 7202])).
% 1.73/2.00 tff(7204,plain,
% 1.73/2.00 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7090, 979, 740])).
% 1.73/2.00 tff(7205,plain,
% 1.73/2.00 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1515, 7204])).
% 1.73/2.00 tff(7206,plain,
% 1.73/2.00 (~b(s(s(s(z))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[6239, 245, 6306, 7205, 709])).
% 1.73/2.00 tff(7207,plain,
% 1.73/2.00 (~r(s(s(s(z))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[985, 979, 220])).
% 1.73/2.00 tff(7208,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[895, 32, 7207, 892, 7206])).
% 1.73/2.00 tff(7209,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(7210,plain,
% 1.73/2.00 (~r(s(s(s(z))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7209, 7139, 7137, 7203, 7132])).
% 1.73/2.00 tff(7211,plain,
% 1.73/2.00 (b(s(s(s(z))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7060, 7210])).
% 1.73/2.00 tff(7212,plain,
% 1.73/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), 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))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7213,plain,
% 1.73/2.00 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7214,plain,
% 1.73/2.00 (((~![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(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7213])).
% 1.73/2.00 tff(7215,plain,
% 1.73/2.00 (((~![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(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[7214, 7212])).
% 1.73/2.00 tff(7216,plain,
% 1.73/2.00 ((~![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(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(7217,plain,
% 1.73/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7216, 7215])).
% 1.73/2.00 tff(7218,plain,
% 1.73/2.00 ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7217, 141, 7203])).
% 1.73/2.00 tff(7219,plain,
% 1.73/2.00 (~r(s(s(s(elem!1))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7218, 7149])).
% 1.73/2.00 tff(7220,plain,
% 1.73/2.00 (b(s(s(s(elem!1))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[37, 7219])).
% 1.73/2.00 tff(7221,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7222,plain,
% 1.73/2.00 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(7223,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[7222])).
% 1.73/2.00 tff(7224,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[7223, 7221])).
% 1.73/2.00 tff(7225,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(7226,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[7225, 7224])).
% 1.73/2.00 tff(7227,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7226, 245, 4105, 4186, 7220, 7211, 7201])).
% 1.73/2.00 tff(7228,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(7229,plain,
% 1.73/2.00 (~r(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[7228, 6596, 6859, 5447, 1277, 96])).
% 1.73/2.00 tff(7230,plain,
% 1.73/2.00 (b(s(z), elem!1)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[389, 7229, 5457])).
% 1.73/2.00 tff(7231,plain,
% 1.73/2.00 (~b(s(z), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4436, 447, 4105, 4186])).
% 1.73/2.00 tff(7232,plain,
% 1.73/2.00 (r(s(z), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[232, 7231])).
% 1.73/2.00 tff(7233,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.73/2.01 tff(7234,plain,
% 1.73/2.01 (b(s(s(s(z))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[895, 32, 7233, 892])).
% 1.73/2.01 tff(7235,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7236,plain,
% 1.73/2.01 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7237,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[7236])).
% 1.73/2.01 tff(7238,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[7237, 7235])).
% 1.73/2.01 tff(7239,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(7240,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[7239, 7238])).
% 1.73/2.01 tff(7241,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7240, 245, 4105, 4186, 447, 954, 7234])).
% 1.73/2.01 tff(7242,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(7243,plain,
% 1.73/2.01 (r(s(s(s(z))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7242, 954, 4186, 447, 4105])).
% 1.73/2.01 tff(7244,plain,
% 1.73/2.01 (~r(s(s(s(z))), z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[985, 7243, 7232])).
% 1.73/2.01 tff(7245,plain,
% 1.73/2.01 (b(s(s(s(z))), z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7060, 7244])).
% 1.73/2.01 tff(7246,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7247,plain,
% 1.73/2.01 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7248,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[7247])).
% 1.73/2.01 tff(7249,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[7248, 7246])).
% 1.73/2.01 tff(7250,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(7251,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[7250, 7249])).
% 1.73/2.01 tff(7252,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7251, 245, 4105, 4186, 7245, 954])).
% 1.73/2.01 tff(7253,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(7254,plain,
% 1.73/2.01 (~b(s(s(s(z))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7253, 6596, 6859, 7230])).
% 1.73/2.01 tff(7255,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.73/2.01 tff(7256,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[6065, 32, 853, 7255, 6213])).
% 1.73/2.01 tff(7257,plain,(b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(7258,plain,
% 1.73/2.01 (r(s(s(s(z))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7257, 7254, 5453])).
% 1.73/2.01 tff(7259,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[822, 141, 572, 816, 930])).
% 1.73/2.01 tff(7260,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(7261,plain,
% 1.73/2.01 (~r(s(elem!1), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7260, 7258, 1277])).
% 1.73/2.01 tff(7262,plain,
% 1.73/2.01 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[582])).
% 1.73/2.01 tff(7263,plain,
% 1.73/2.01 (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[7262, 313])).
% 1.73/2.01 tff(7264,plain,
% 1.73/2.01 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2163, 6873])).
% 1.73/2.01 tff(7265,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7264, 7263])).
% 1.73/2.01 tff(7266,plain,((~(s(elem!1) = s(s(s(z))))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(7267,plain,
% 1.73/2.01 (~(s(elem!1) = s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7266, 5447])).
% 1.73/2.01 tff(7268,plain,
% 1.73/2.01 (b(s(elem!1), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[826, 32, 7267, 7261])).
% 1.73/2.01 tff(7269,plain,
% 1.73/2.01 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1051, 5447])).
% 1.73/2.01 tff(7270,plain,
% 1.73/2.01 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[775, 7269])).
% 1.73/2.01 tff(7271,plain,
% 1.73/2.01 (~b(z, s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[6989, 245, 4105, 4186, 4878])).
% 1.73/2.01 tff(7272,plain,
% 1.73/2.01 (r(z, s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[758, 7271])).
% 1.73/2.01 tff(7273,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7274,plain,
% 1.73/2.01 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7275,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[7274])).
% 1.73/2.01 tff(7276,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[7275, 7273])).
% 1.73/2.01 tff(7277,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(7278,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[7277, 7276])).
% 1.73/2.01 tff(7279,plain,
% 1.73/2.01 (~b(s(z), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7278, 245, 4105, 4186, 447, 4878])).
% 1.73/2.01 tff(7280,plain,
% 1.73/2.01 (r(s(z), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1698, 7279])).
% 1.73/2.01 tff(7281,plain,
% 1.73/2.01 (~b(z, s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4595, 447, 4105, 4186])).
% 1.73/2.01 tff(7282,plain,
% 1.73/2.01 (r(z, s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1421, 7281])).
% 1.73/2.01 tff(7283,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[6833, 141, 7282, 7280, 7272])).
% 1.73/2.01 tff(7284,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(7285,plain,
% 1.73/2.01 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7284, 7230, 6859, 6596])).
% 1.73/2.01 tff(7286,plain,
% 1.73/2.01 (r(s(s(s(s(s(z))))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[787, 7285, 7270])).
% 1.73/2.01 tff(7287,plain,
% 1.73/2.01 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[6891, 141, 1277, 7286])).
% 1.73/2.01 tff(7288,plain,
% 1.73/2.01 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = z)),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5447])).
% 1.73/2.01 tff(7289,plain,
% 1.73/2.01 ((s(s(s(s(elem!1)))) = z) <=> (z = elem!1)),
% 1.73/2.01 inference(transitivity,[status(thm)],[7288, 119])).
% 1.73/2.01 tff(7290,plain,
% 1.73/2.01 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = elem!1))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[7289])).
% 1.73/2.01 tff(7291,plain,
% 1.73/2.01 (~(z = elem!1)),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[66, 7290])).
% 1.73/2.01 tff(7292,plain,
% 1.73/2.01 (~(s(z) = s(elem!1))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[57, 7291])).
% 1.73/2.01 tff(7293,plain,
% 1.73/2.01 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1065, 7292, 5447])).
% 1.73/2.01 tff(7294,plain,
% 1.73/2.01 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1156, 32, 7293, 7287])).
% 1.73/2.01 tff(7295,plain,
% 1.73/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7296,plain,
% 1.73/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(7297,plain,
% 1.73/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[7296, 7295])).
% 1.73/2.01 tff(7298,plain,
% 1.73/2.01 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7297, 141, 7258, 7286])).
% 1.73/2.01 tff(7299,plain,
% 1.73/2.01 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[909, 7298])).
% 1.73/2.01 tff(7300,plain,
% 1.73/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(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))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7301,plain,
% 1.73/2.01 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7302,plain,
% 1.73/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[7301])).
% 1.73/2.01 tff(7303,plain,
% 1.73/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[7302, 7300])).
% 1.73/2.01 tff(7304,plain,
% 1.73/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(7305,plain,
% 1.73/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[7304, 7303])).
% 1.73/2.01 tff(7306,plain,
% 1.73/2.01 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7305, 141, 7258, 7286])).
% 1.73/2.01 tff(7307,plain,
% 1.73/2.01 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1515, 7306])).
% 1.73/2.01 tff(7308,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7309,plain,
% 1.73/2.01 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(7310,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[7309])).
% 1.73/2.01 tff(7311,plain,
% 1.73/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[7310, 7308])).
% 1.73/2.01 tff(7312,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(7313,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[7312, 7311])).
% 1.73/2.01 tff(7314,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7313, 245, 7307, 7299, 7294, 7268])).
% 1.73/2.01 tff(7315,plain,(b(s(elem!1), elem!1) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(7316,plain,
% 1.73/2.01 (b(s(elem!1), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[7315, 1])).
% 1.73/2.01 tff(7317,plain,
% 1.73/2.01 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[39])).
% 1.73/2.01 tff(7318,plain,
% 1.73/2.01 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.73/2.01 inference(transitivity,[status(thm)],[7317, 1939])).
% 1.73/2.02 tff(7319,plain,
% 1.73/2.02 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7318, 1940])).
% 1.73/2.02 tff(7320,plain,
% 1.73/2.02 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7319])).
% 1.73/2.02 tff(7321,plain,
% 1.73/2.02 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[1128, 7320])).
% 1.73/2.02 tff(7322,plain,
% 1.73/2.02 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7318])).
% 1.73/2.02 tff(7323,plain,
% 1.73/2.02 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[1128, 7322])).
% 1.73/2.02 tff(7324,plain,
% 1.73/2.02 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[331, 7323])).
% 1.73/2.02 tff(7325,plain,
% 1.73/2.02 (r(z, s(elem!1)) <=> r(z, s(z))),
% 1.73/2.02 inference(symmetry,[status(thm)],[1423])).
% 1.73/2.02 tff(7326,plain,
% 1.73/2.02 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.73/2.02 inference(transitivity,[status(thm)],[1332, 7325])).
% 1.73/2.02 tff(7327,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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(X0, 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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7328,plain,
% 1.73/2.02 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7329,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(X0, 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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7328])).
% 1.73/2.02 tff(7330,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(X0, 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)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7329, 7327])).
% 1.73/2.02 tff(7331,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), 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))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(7332,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7331, 7330])).
% 1.73/2.02 tff(7333,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7332, 245, 308, 1103, 2824, 10])).
% 1.73/2.02 tff(7334,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(7335,plain,
% 1.73/2.02 (~b(elem!1, s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7334, 10, 7316, 2824])).
% 1.73/2.02 tff(7336,plain,
% 1.73/2.02 (r(elem!1, s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2777, 7335, 2563])).
% 1.73/2.02 tff(7337,plain,
% 1.73/2.02 (r(z, s(z))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7336, 7326])).
% 1.73/2.02 tff(7338,plain,
% 1.73/2.02 (~r(s(s(s(elem!1))), s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1457, 7337, 1355])).
% 1.73/2.02 tff(7339,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[265, 7338])).
% 1.73/2.02 tff(7340,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(elem!1))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7339, 1338])).
% 1.73/2.02 tff(7341,plain,
% 1.73/2.02 (r(s(s(s(elem!1))), elem!1)),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[1355, 1335])).
% 1.73/2.02 tff(7342,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7343,plain,
% 1.73/2.02 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7344,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7343])).
% 1.73/2.02 tff(7345,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7344, 7342])).
% 1.73/2.02 tff(7346,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(7347,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7346, 7345])).
% 1.73/2.02 tff(7348,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7347, 245, 1390, 308, 2824, 10])).
% 1.73/2.02 tff(7349,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(7350,plain,
% 1.73/2.02 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7349, 10, 2824, 7316])).
% 1.73/2.02 tff(7351,plain,
% 1.73/2.02 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1432, 7350, 67])).
% 1.73/2.02 tff(7352,plain,
% 1.73/2.02 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[3538, 7351, 7341])).
% 1.73/2.02 tff(7353,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1239, 7352, 1304])).
% 1.73/2.02 tff(7354,plain,
% 1.73/2.02 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1376, 7351, 7336])).
% 1.73/2.02 tff(7355,plain,
% 1.73/2.02 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1263, 7354, 1])).
% 1.73/2.02 tff(7356,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1295, 7355, 7353, 7340, 10])).
% 1.73/2.02 tff(7357,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(7358,plain,
% 1.73/2.02 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7357, 2824, 1, 39, 1355])).
% 1.73/2.02 tff(7359,plain,
% 1.73/2.02 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[420, 7358, 7])).
% 1.73/2.02 tff(7360,plain,
% 1.73/2.02 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2058, 141, 371, 406])).
% 1.73/2.02 tff(7361,plain,
% 1.73/2.02 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[415, 371, 406])).
% 1.73/2.02 tff(7362,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1239, 7361, 1309])).
% 1.73/2.02 tff(7363,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7364,plain,
% 1.73/2.02 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7365,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7364])).
% 1.73/2.02 tff(7366,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7365, 7363])).
% 1.73/2.02 tff(7367,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(7368,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7367, 7366])).
% 1.73/2.02 tff(7369,plain,
% 1.73/2.02 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7368, 245, 2101, 2824, 7362])).
% 1.73/2.02 tff(7370,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1320, 7369, 7360, 3067])).
% 1.73/2.02 tff(7371,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(7372,plain,
% 1.73/2.02 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7371, 2101, 2824, 406, 1309])).
% 1.73/2.02 tff(7373,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(elem!1))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[353, 7372, 11])).
% 1.73/2.02 tff(7374,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1715, 245, 7373, 308, 1103, 2101])).
% 1.73/2.02 tff(7375,plain,((~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)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(7376,plain,
% 1.73/2.02 (~b(elem!1, s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7375, 1103, 7316, 7323, 2824, 406, 1304])).
% 1.73/2.02 tff(7377,plain,
% 1.73/2.02 (r(elem!1, s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1724, 7376, 1673])).
% 1.73/2.02 tff(7378,plain,
% 1.73/2.02 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.73/2.02 inference(monotonicity,[status(thm)],[58])).
% 1.73/2.02 tff(7379,plain,
% 1.73/2.02 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7378, 686])).
% 1.73/2.02 tff(7380,plain,
% 1.73/2.02 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7379])).
% 1.73/2.02 tff(7381,plain,
% 1.73/2.02 (~(elem!1 = s(s(s(z))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[833, 7380])).
% 1.73/2.02 tff(7382,plain,
% 1.73/2.02 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[1492])).
% 1.73/2.02 tff(7383,plain,
% 1.73/2.02 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.73/2.02 inference(symmetry,[status(thm)],[7382])).
% 1.73/2.02 tff(7384,plain,
% 1.73/2.02 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7383])).
% 1.73/2.02 tff(7385,plain,
% 1.73/2.02 (~b(elem!1, s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7375, 1103, 308, 7323, 2824, 406, 1309])).
% 1.73/2.02 tff(7386,plain,
% 1.73/2.02 (~b(elem!1, s(s(s(z))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7385, 7384])).
% 1.73/2.02 tff(7387,plain,
% 1.73/2.02 (r(elem!1, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[967, 7386, 7381])).
% 1.73/2.02 tff(7388,plain,
% 1.73/2.02 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[1492])).
% 1.73/2.02 tff(7389,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.02 inference(symmetry,[status(thm)],[7388])).
% 1.73/2.02 tff(7390,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[1495])).
% 1.73/2.02 tff(7391,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7390, 7389])).
% 1.73/2.02 tff(7392,plain,
% 1.73/2.02 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7391])).
% 1.73/2.02 tff(7393,plain,
% 1.73/2.02 ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) <=> (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[4045])).
% 1.73/2.02 tff(7394,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(symmetry,[status(thm)],[7390])).
% 1.73/2.02 tff(7395,plain,
% 1.73/2.02 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7388, 7394])).
% 1.73/2.02 tff(7396,plain,
% 1.73/2.02 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[3068, 1739])).
% 1.73/2.02 tff(7397,plain,
% 1.73/2.02 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1746, 141, 406, 3024])).
% 1.73/2.02 tff(7398,plain,
% 1.73/2.02 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1750, 32, 7397])).
% 1.73/2.02 tff(7399,plain,
% 1.73/2.02 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7398, 7396])).
% 1.73/2.02 tff(7400,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.73/2.02 tff(7401,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7402,plain,
% 1.73/2.02 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(7403,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7402])).
% 1.73/2.02 tff(7404,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.73/2.02 inference(transitivity,[status(thm)],[7403, 7401])).
% 1.73/2.02 tff(7405,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(7406,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7405, 7404])).
% 1.73/2.02 tff(7407,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7406, 245, 308, 1103, 2824, 1543, 7400])).
% 1.73/2.02 tff(7408,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(7409,plain,
% 1.73/2.02 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7408, 7399, 1103, 2824, 308])).
% 1.73/2.02 tff(7410,plain,
% 1.73/2.02 (s(s(z)) = s(s(elem!1))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[3890])).
% 1.73/2.02 tff(7411,plain,
% 1.73/2.02 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7410])).
% 1.73/2.02 tff(7412,plain,
% 1.73/2.02 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7411])).
% 1.73/2.02 tff(7413,plain,
% 1.73/2.02 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7412])).
% 1.73/2.02 tff(7414,plain,
% 1.73/2.02 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.73/2.02 inference(symmetry,[status(thm)],[7413])).
% 1.73/2.02 tff(7415,plain,
% 1.73/2.02 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.73/2.02 inference(monotonicity,[status(thm)],[7414, 120])).
% 1.73/2.02 tff(7416,plain,
% 1.73/2.02 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/2.02 inference(symmetry,[status(thm)],[7415])).
% 1.73/2.02 tff(7417,plain,
% 1.73/2.02 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.73/2.02 inference(monotonicity,[status(thm)],[120])).
% 1.73/2.02 tff(7418,plain,
% 1.73/2.02 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/2.02 inference(transitivity,[status(thm)],[7417, 7416])).
% 1.73/2.02 tff(7419,plain,
% 1.73/2.02 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[4878, 7418])).
% 1.73/2.02 tff(7420,assumption,(~b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.73/2.02 tff(7421,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7420, 7419])).
% 1.73/2.02 tff(7422,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(7423,plain,
% 1.73/2.02 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[7422, 7409, 3858])).
% 1.73/2.02 tff(7424,plain,
% 1.73/2.02 (r(s(s(s(s(s(z))))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[787, 7423, 3029])).
% 1.73/2.02 tff(7425,plain,
% 1.73/2.02 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[3714, 7424, 39])).
% 1.73/2.02 tff(7426,plain,
% 1.73/2.02 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1507, 141, 170, 7425])).
% 1.73/2.02 tff(7427,plain,
% 1.73/2.02 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7426, 1500])).
% 1.73/2.02 tff(7428,plain,
% 1.73/2.02 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1515, 7427])).
% 1.73/2.02 tff(7429,plain,
% 1.73/2.02 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[7428, 7395])).
% 1.73/2.02 tff(7430,plain,
% 1.73/2.02 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1593, 141, 406, 3024])).
% 1.85/2.02 tff(7431,plain,
% 1.85/2.02 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[1526, 32, 3068, 7430])).
% 1.85/2.02 tff(7432,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(7433,plain,
% 1.85/2.02 (((~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)))))) | (~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(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(7434,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(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)))))) | (~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(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))))))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[7433])).
% 1.85/2.02 tff(7435,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(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)))))) | (~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(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))))))),
% 1.85/2.02 inference(transitivity,[status(thm)],[7434, 7432])).
% 1.85/2.02 tff(7436,plain,
% 1.85/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(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)))))) | (~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(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(7437,plain,
% 1.85/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))))))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[7436, 7435])).
% 1.85/2.02 tff(7438,plain,
% 1.85/2.02 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7437, 245, 7431, 7399, 7429])).
% 1.85/2.03 tff(7439,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1239, 7438, 1309])).
% 1.85/2.03 tff(7440,plain,
% 1.85/2.03 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2357, 7439, 1366])).
% 1.85/2.03 tff(7441,plain,
% 1.85/2.03 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2091, 32, 7440, 7321])).
% 1.85/2.03 tff(7442,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[1492])).
% 1.85/2.03 tff(7443,plain,
% 1.85/2.03 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3538, 7439, 170])).
% 1.85/2.03 tff(7444,plain,
% 1.85/2.03 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1432, 7443, 67])).
% 1.85/2.03 tff(7445,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3763, 7444, 7324, 1555, 2824, 2070, 7439])).
% 1.85/2.03 tff(7446,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[4079, 7445, 39])).
% 1.85/2.03 tff(7447,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1630, 7446, 1616])).
% 1.85/2.03 tff(7448,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7447, 7442])).
% 1.85/2.03 tff(7449,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7450,plain,
% 1.85/2.03 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7451,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[7450])).
% 1.85/2.03 tff(7452,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[7451, 7449])).
% 1.85/2.03 tff(7453,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(7454,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7453, 7452])).
% 1.85/2.03 tff(7455,plain,
% 1.85/2.03 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7454, 245, 1287, 308, 7448])).
% 1.85/2.03 tff(7456,plain,
% 1.85/2.03 (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7455, 7441])).
% 1.85/2.03 tff(7457,plain,
% 1.85/2.03 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7456, 7393])).
% 1.85/2.03 tff(7458,plain,
% 1.85/2.03 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[470, 7457])).
% 1.85/2.03 tff(7459,plain,
% 1.85/2.03 (r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7458, 4047])).
% 1.85/2.03 tff(7460,plain,
% 1.85/2.03 (((~![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(elem!1))))), 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(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7461,plain,
% 1.85/2.03 ((~![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(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(7462,plain,
% 1.85/2.03 ((~![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(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7461, 7460])).
% 1.85/2.03 tff(7463,plain,
% 1.85/2.03 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7462, 141, 170, 7425])).
% 1.85/2.03 tff(7464,plain,
% 1.85/2.03 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7463, 1834])).
% 1.85/2.03 tff(7465,plain,
% 1.85/2.03 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[909, 7464])).
% 1.85/2.03 tff(7466,plain,
% 1.85/2.03 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7465, 1833])).
% 1.85/2.03 tff(7467,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7468,plain,
% 1.85/2.03 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7469,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(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(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[7468])).
% 1.85/2.03 tff(7470,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(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(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[7469, 7467])).
% 1.85/2.03 tff(7471,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(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(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(7472,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7471, 7470])).
% 1.85/2.03 tff(7473,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7472, 245, 7448, 7429, 7466])).
% 1.85/2.03 tff(7474,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1607, 32, 3972, 7473])).
% 1.85/2.03 tff(7475,plain,
% 1.85/2.03 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[1643])).
% 1.85/2.03 tff(7476,plain,
% 1.85/2.03 (r(z, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(symmetry,[status(thm)],[7475])).
% 1.85/2.03 tff(7477,plain,
% 1.85/2.03 (r(z, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[58, 1495])).
% 1.85/2.03 tff(7478,plain,
% 1.85/2.03 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(symmetry,[status(thm)],[7477])).
% 1.85/2.03 tff(7479,plain,
% 1.85/2.03 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[1644, 1646])).
% 1.85/2.03 tff(7480,plain,
% 1.85/2.03 ((~b(elem!1, s(s(s(s(s(elem!1))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[7479])).
% 1.85/2.03 tff(7481,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7482,plain,
% 1.85/2.03 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(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(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, 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))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7483,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(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(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[7482])).
% 1.85/2.03 tff(7484,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(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(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[7483, 7481])).
% 1.85/2.03 tff(7485,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(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(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(7486,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7485, 7484])).
% 1.85/2.03 tff(7487,plain,
% 1.85/2.03 ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7486, 245, 1103, 2824, 7431])).
% 1.85/2.03 tff(7488,plain,
% 1.85/2.03 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7487, 7444])).
% 1.85/2.03 tff(7489,plain,
% 1.85/2.03 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7488, 7480])).
% 1.85/2.03 tff(7490,plain,
% 1.85/2.03 (r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[720, 7489, 1652])).
% 1.85/2.03 tff(7491,plain,
% 1.85/2.03 (r(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7490, 7478])).
% 1.85/2.03 tff(7492,plain,
% 1.85/2.03 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7491, 7476])).
% 1.85/2.03 tff(7493,plain,
% 1.85/2.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(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(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7494,plain,
% 1.85/2.03 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7495,plain,
% 1.85/2.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[7494])).
% 1.85/2.03 tff(7496,plain,
% 1.85/2.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[7495, 7493])).
% 1.85/2.03 tff(7497,plain,
% 1.85/2.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(7498,plain,
% 1.85/2.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7497, 7496])).
% 1.85/2.03 tff(7499,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7498, 141, 7492, 7474])).
% 1.85/2.03 tff(7500,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1768, 7499, 1555])).
% 1.85/2.03 tff(7501,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7502,plain,
% 1.85/2.03 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7503,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[7502])).
% 1.85/2.03 tff(7504,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[7503, 7501])).
% 1.85/2.03 tff(7505,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(7506,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[7505, 7504])).
% 1.85/2.03 tff(7507,plain,
% 1.85/2.03 ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7506, 245, 7444, 7448, 7399, 7466])).
% 1.85/2.03 tff(7508,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[7507, 7500])).
% 1.85/2.03 tff(7509,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[501, 7508, 7324])).
% 1.85/2.03 tff(7510,assumption,(r(s(elem!1), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.85/2.03 tff(7511,plain,
% 1.85/2.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(7512,plain,
% 1.85/2.03 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7513,plain,
% 1.85/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(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(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[7512])).
% 1.85/2.04 tff(7514,plain,
% 1.85/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(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(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[7513, 7511])).
% 1.85/2.04 tff(7515,plain,
% 1.85/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(7516,plain,
% 1.85/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7515, 7514])).
% 1.85/2.04 tff(7517,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7516, 141, 1366, 529, 7510])).
% 1.85/2.04 tff(7518,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(7519,plain,
% 1.85/2.04 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7518, 7509, 1366])).
% 1.85/2.04 tff(7520,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7519, 7459])).
% 1.85/2.04 tff(7521,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(7522,plain,
% 1.85/2.04 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7521, 1287, 1366, 39, 308, 1616, 1103, 2824, 2070, 170, 1309, 406])).
% 1.85/2.04 tff(7523,plain,
% 1.85/2.04 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3059, 7522, 3066])).
% 1.85/2.04 tff(7524,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7525,plain,
% 1.85/2.04 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7526,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[7525])).
% 1.85/2.04 tff(7527,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[7526, 7524])).
% 1.85/2.04 tff(7528,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(7529,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7528, 7527])).
% 1.85/2.04 tff(7530,plain,
% 1.85/2.04 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7529, 245, 1287, 308, 1103, 7523])).
% 1.85/2.04 tff(7531,plain,
% 1.85/2.04 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7530, 7392])).
% 1.85/2.04 tff(7532,plain,
% 1.85/2.04 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1515, 7531])).
% 1.85/2.04 tff(7533,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7534,plain,
% 1.85/2.04 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7535,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[7534])).
% 1.85/2.04 tff(7536,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[7535, 7533])).
% 1.85/2.04 tff(7537,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(7538,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7537, 7536])).
% 1.85/2.04 tff(7539,plain,
% 1.85/2.04 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7538, 245, 308, 1103, 7523])).
% 1.85/2.04 tff(7540,plain,
% 1.85/2.04 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7539, 7480])).
% 1.85/2.04 tff(7541,plain,
% 1.85/2.04 (r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[720, 7540, 1652])).
% 1.85/2.04 tff(7542,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.85/2.04 tff(7543,plain,
% 1.85/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7544,plain,
% 1.85/2.04 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7545,plain,
% 1.85/2.04 (((~![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(elem!1, 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(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[7544])).
% 1.85/2.04 tff(7546,plain,
% 1.85/2.04 (((~![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(elem!1, 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(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[7545, 7543])).
% 1.85/2.04 tff(7547,plain,
% 1.85/2.04 ((~![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(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(7548,plain,
% 1.85/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7547, 7546])).
% 1.85/2.04 tff(7549,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7548, 141, 7542, 723, 6013])).
% 1.85/2.04 tff(7550,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(7551,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7550, 7541, 7532, 7387])).
% 1.85/2.04 tff(7552,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(7553,plain,
% 1.85/2.04 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7552, 1103, 7316, 39, 1366, 1572, 2824, 7377, 170, 1304, 406])).
% 1.85/2.04 tff(7554,plain,
% 1.85/2.04 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[353, 7553, 7323])).
% 1.85/2.04 tff(7555,plain,
% 1.85/2.04 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[415, 7554, 406])).
% 1.85/2.04 tff(7556,plain,
% 1.85/2.04 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1239, 7555, 1304])).
% 1.85/2.04 tff(7557,plain,
% 1.85/2.04 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2058, 141, 7554, 406])).
% 1.85/2.04 tff(7558,plain,
% 1.85/2.04 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1320, 7557, 1312])).
% 1.85/2.04 tff(7559,plain,
% 1.85/2.04 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1823, 7558, 7316, 406, 2692, 1103, 7556, 39, 1])).
% 1.85/2.04 tff(7560,plain,
% 1.85/2.04 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7422, 7559, 3858])).
% 1.85/2.04 tff(7561,plain,
% 1.85/2.04 (r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[787, 7560, 3029])).
% 1.85/2.04 tff(7562,plain,
% 1.85/2.04 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3714, 7561, 39])).
% 1.85/2.04 tff(7563,plain,
% 1.85/2.04 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7462, 141, 170, 7562])).
% 1.85/2.04 tff(7564,plain,
% 1.85/2.04 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7563, 1834])).
% 1.85/2.04 tff(7565,plain,
% 1.85/2.04 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[909, 7564])).
% 1.85/2.04 tff(7566,plain,
% 1.85/2.04 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7565, 1833])).
% 1.85/2.04 tff(7567,plain,
% 1.85/2.04 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1507, 141, 170, 7562])).
% 1.85/2.04 tff(7568,plain,
% 1.85/2.04 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7567, 1500])).
% 1.85/2.04 tff(7569,plain,
% 1.85/2.04 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1515, 7568])).
% 1.85/2.04 tff(7570,plain,
% 1.85/2.04 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7569, 7388])).
% 1.85/2.04 tff(7571,plain,
% 1.85/2.04 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7570, 7394])).
% 1.85/2.04 tff(7572,plain,
% 1.85/2.04 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[1682])).
% 1.85/2.04 tff(7573,plain,
% 1.85/2.04 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[2639, 2638, 7572])).
% 1.85/2.04 tff(7574,plain,
% 1.85/2.04 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[39])).
% 1.85/2.04 tff(7575,plain,
% 1.85/2.04 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[7574])).
% 1.85/2.04 tff(7576,plain,
% 1.85/2.04 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[1495])).
% 1.85/2.04 tff(7577,plain,
% 1.85/2.04 (r(s(elem!1), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[7576, 7575])).
% 1.85/2.04 tff(7578,plain,
% 1.85/2.04 ((~r(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~r(s(z), s(s(s(s(s(z)))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[7577])).
% 1.85/2.04 tff(7579,plain,
% 1.85/2.04 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1846, 245, 7558, 7556])).
% 1.85/2.04 tff(7580,plain,
% 1.85/2.04 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7579, 7566])).
% 1.85/2.04 tff(7581,plain,
% 1.85/2.04 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1526, 32, 7580, 1490])).
% 1.85/2.04 tff(7582,plain,
% 1.85/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7583,plain,
% 1.85/2.04 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7584,plain,
% 1.85/2.04 (((~![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(elem!1), s(s(s(s(elem!1)))))) | (~r(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[7583])).
% 1.85/2.04 tff(7585,plain,
% 1.85/2.04 (((~![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(elem!1), s(s(s(s(elem!1)))))) | (~r(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[7584, 7582])).
% 1.85/2.04 tff(7586,plain,
% 1.85/2.04 ((~![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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(7587,plain,
% 1.85/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7586, 7585])).
% 1.85/2.04 tff(7588,plain,
% 1.85/2.04 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7587, 141, 1366, 7581])).
% 1.85/2.04 tff(7589,plain,
% 1.85/2.04 (~r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7588, 7578])).
% 1.85/2.04 tff(7590,plain,
% 1.85/2.04 (b(s(z), s(s(s(s(s(z))))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1698, 7589])).
% 1.85/2.04 tff(7591,plain,
% 1.85/2.04 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7590, 7573])).
% 1.85/2.04 tff(7592,plain,
% 1.85/2.04 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3048, 141, 1366, 7581])).
% 1.85/2.04 tff(7593,plain,
% 1.85/2.04 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[3059, 7592, 3066])).
% 1.85/2.04 tff(7594,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7595,plain,
% 1.85/2.04 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7596,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[7595])).
% 1.85/2.04 tff(7597,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[7596, 7594])).
% 1.85/2.04 tff(7598,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(7599,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7598, 7597])).
% 1.85/2.04 tff(7600,plain,
% 1.85/2.04 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7599, 245, 7316, 7593, 7591, 7571])).
% 1.85/2.04 tff(7601,plain,
% 1.85/2.04 (r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2091, 32, 7600, 7321])).
% 1.85/2.04 tff(7602,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2525, 141, 2133, 3753])).
% 1.85/2.04 tff(7603,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7602, 1780])).
% 1.85/2.04 tff(7604,plain,
% 1.85/2.04 (((~![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(elem!1)))))), elem!1)) | (~r(s(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(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7605,plain,
% 1.85/2.04 ((~![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(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(7606,plain,
% 1.85/2.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7605, 7604])).
% 1.85/2.04 tff(7607,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7606, 141, 170, 2700, 3753])).
% 1.85/2.04 tff(7608,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(7609,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7608, 3753, 170])).
% 1.85/2.04 tff(7610,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1768, 7609, 1555])).
% 1.85/2.04 tff(7611,plain,
% 1.85/2.04 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1775, 245, 308, 1103, 7610])).
% 1.85/2.04 tff(7612,plain,
% 1.85/2.04 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7611, 1546])).
% 1.85/2.04 tff(7613,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1820, 7612, 7603])).
% 1.85/2.04 tff(7614,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(7615,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[7614, 1103, 7316, 39, 7601, 170])).
% 1.85/2.04 tff(7616,plain,
% 1.85/2.04 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4079, 7615, 39])).
% 1.85/2.04 tff(7617,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1630, 7616, 1572])).
% 1.85/2.04 tff(7618,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[7617, 7442])).
% 1.85/2.04 tff(7619,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7620,plain,
% 1.85/2.04 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(7621,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7620])).
% 1.85/2.05 tff(7622,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[7621, 7619])).
% 1.85/2.05 tff(7623,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(7624,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7623, 7622])).
% 1.85/2.05 tff(7625,plain,
% 1.85/2.05 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7624, 245, 7558, 7556, 7618, 7566])).
% 1.85/2.05 tff(7626,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1607, 32, 2692, 7625])).
% 1.85/2.05 tff(7627,plain,
% 1.85/2.05 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7628,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7627])).
% 1.85/2.05 tff(7629,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[7628, 1619])).
% 1.85/2.05 tff(7630,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(7631,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7630, 7629])).
% 1.85/2.05 tff(7632,plain,
% 1.85/2.05 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7631, 245, 7558, 7556, 7618])).
% 1.85/2.05 tff(7633,plain,
% 1.85/2.05 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[501, 7632, 7324])).
% 1.85/2.05 tff(7634,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1852, 141, 7633, 7581, 7626])).
% 1.85/2.05 tff(7635,plain,((~b(elem!1, s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7636,plain,
% 1.85/2.05 (~b(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7635, 1366, 7341, 39, 7359, 1, 2824])).
% 1.85/2.05 tff(7637,plain,
% 1.85/2.05 (r(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2777, 7636, 2563])).
% 1.85/2.05 tff(7638,plain,
% 1.85/2.05 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1376, 7637, 1366])).
% 1.85/2.05 tff(7639,plain,
% 1.85/2.05 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1432, 7638, 67])).
% 1.85/2.05 tff(7640,plain,
% 1.85/2.05 (r(z, s(z))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7637, 7326])).
% 1.85/2.05 tff(7641,plain,
% 1.85/2.05 (~r(s(s(s(elem!1))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1457, 7640, 1355])).
% 1.85/2.05 tff(7642,plain,
% 1.85/2.05 (b(s(s(s(elem!1))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[265, 7641])).
% 1.85/2.05 tff(7643,plain,
% 1.85/2.05 (b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7642, 1338])).
% 1.85/2.05 tff(7644,plain,
% 1.85/2.05 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[3236, 7643, 39, 2824, 1490, 7359, 1572, 7637, 7639, 7324])).
% 1.85/2.05 tff(7645,plain,
% 1.85/2.05 (r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2091, 32, 7644, 7321])).
% 1.85/2.05 tff(7646,plain,
% 1.85/2.05 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2357, 7645, 1366])).
% 1.85/2.05 tff(7647,plain,
% 1.85/2.05 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1239, 7646, 1304])).
% 1.85/2.05 tff(7648,plain,
% 1.85/2.05 (~b(elem!1, s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[5387, 245, 7639, 2824, 7647])).
% 1.85/2.05 tff(7649,plain,
% 1.85/2.05 (r(elem!1, s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1724, 7648, 1673])).
% 1.85/2.05 tff(7650,plain,
% 1.85/2.05 (((~![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(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(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7651,plain,
% 1.85/2.05 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7652,plain,
% 1.85/2.05 (((~![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(elem!1, s(s(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(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7651])).
% 1.85/2.05 tff(7653,plain,
% 1.85/2.05 (((~![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(elem!1, s(s(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(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[7652, 7650])).
% 1.85/2.05 tff(7654,plain,
% 1.85/2.05 ((~![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(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(7655,plain,
% 1.85/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7654, 7653])).
% 1.85/2.05 tff(7656,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7655, 141, 7637, 7649, 7645])).
% 1.85/2.05 tff(7657,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7658,plain,
% 1.85/2.05 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7657, 2561, 39, 38, 1])).
% 1.85/2.05 tff(7659,plain,
% 1.85/2.05 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1263, 7658, 1])).
% 1.85/2.05 tff(7660,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7661,plain,
% 1.85/2.05 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7662,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7661])).
% 1.85/2.05 tff(7663,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[7662, 7660])).
% 1.85/2.05 tff(7664,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), 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(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(7665,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7664, 7663])).
% 1.85/2.05 tff(7666,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7665, 245, 1390, 308, 2824, 556])).
% 1.85/2.05 tff(7667,plain,((~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(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7668,plain,
% 1.85/2.05 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7667, 7659, 7316, 2561])).
% 1.85/2.05 tff(7669,plain,
% 1.85/2.05 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1432, 7668, 67])).
% 1.85/2.05 tff(7670,plain,
% 1.85/2.05 (r(z, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7669, 60])).
% 1.85/2.05 tff(7671,plain,
% 1.85/2.05 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7357, 2561, 1, 39, 38])).
% 1.85/2.05 tff(7672,plain,
% 1.85/2.05 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[420, 7671, 7])).
% 1.85/2.05 tff(7673,plain,
% 1.85/2.05 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[3521, 2561, 58])).
% 1.85/2.05 tff(7674,plain,
% 1.85/2.05 (b(s(z), z) <=> b(s(elem!1), z)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[39])).
% 1.85/2.05 tff(7675,plain,
% 1.85/2.05 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[114])).
% 1.85/2.05 tff(7676,plain,
% 1.85/2.05 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.85/2.05 inference(symmetry,[status(thm)],[7675])).
% 1.85/2.05 tff(7677,plain,
% 1.85/2.05 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.85/2.05 inference(monotonicity,[status(thm)],[39])).
% 1.85/2.05 tff(7678,plain,
% 1.85/2.05 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.85/2.05 inference(symmetry,[status(thm)],[7677])).
% 1.85/2.05 tff(7679,plain,
% 1.85/2.05 (b(s(z), elem!1)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[308, 7678])).
% 1.85/2.05 tff(7680,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.85/2.05 tff(7681,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7680, 7679])).
% 1.85/2.05 tff(7682,plain,((~(s(z) = s(elem!1))) | b(s(z), elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7683,plain,
% 1.85/2.05 (b(s(z), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7682, 3100, 308])).
% 1.85/2.05 tff(7684,plain,
% 1.85/2.05 (b(s(z), z)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7683, 7676])).
% 1.85/2.05 tff(7685,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.85/2.05 tff(7686,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7685, 7684])).
% 1.85/2.05 tff(7687,plain,((~(z = elem!1)) | b(s(z), z) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7688,plain,
% 1.85/2.05 (b(s(z), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7687, 58, 7316])).
% 1.85/2.05 tff(7689,plain,
% 1.85/2.05 (b(s(elem!1), z)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7688, 7674])).
% 1.85/2.05 tff(7690,plain,
% 1.85/2.05 (~b(z, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[3304, 7659, 7689, 7673])).
% 1.85/2.05 tff(7691,plain,
% 1.85/2.05 (r(z, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[644, 7690])).
% 1.85/2.05 tff(7692,plain,
% 1.85/2.05 (~r(z, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[3674, 7691, 7672])).
% 1.85/2.05 tff(7693,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7692, 7670])).
% 1.85/2.05 tff(7694,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7695,plain,
% 1.85/2.05 (~(s(z) = s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7694, 12, 1])).
% 1.85/2.05 tff(7696,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.85/2.05 tff(7697,plain,
% 1.85/2.05 (b(elem!1, z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[128, 124, 7696])).
% 1.85/2.05 tff(7698,plain,
% 1.85/2.05 (~r(z, elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2875, 170, 1355])).
% 1.85/2.05 tff(7699,plain,
% 1.85/2.05 (b(z, elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[175, 7698, 118])).
% 1.85/2.05 tff(7700,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7701,plain,
% 1.85/2.05 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7702,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7701])).
% 1.85/2.05 tff(7703,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.85/2.05 inference(transitivity,[status(thm)],[7702, 7700])).
% 1.85/2.05 tff(7704,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(7705,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), z))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7704, 7703])).
% 1.85/2.05 tff(7706,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7705, 245, 4105, 4186, 308, 288])).
% 1.85/2.05 tff(7707,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7708,plain,
% 1.85/2.05 (~b(s(elem!1), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7707, 308, 4105, 4186])).
% 1.85/2.05 tff(7709,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7710,plain,
% 1.85/2.05 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7711,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7710])).
% 1.85/2.05 tff(7712,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[7711, 7709])).
% 1.85/2.05 tff(7713,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(7714,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7713, 7712])).
% 1.85/2.05 tff(7715,plain,
% 1.85/2.05 (~b(z, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7714, 245, 4105, 4186, 308])).
% 1.85/2.05 tff(7716,plain,
% 1.85/2.05 (r(z, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[644, 7715])).
% 1.85/2.05 tff(7717,assumption,(~r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.05 tff(7718,plain,
% 1.85/2.05 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[3835])).
% 1.85/2.05 tff(7719,plain,
% 1.85/2.05 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(elem!1))),
% 1.85/2.05 inference(symmetry,[status(thm)],[7718])).
% 1.85/2.05 tff(7720,plain,
% 1.85/2.05 ((~r(z, s(s(s(s(elem!1)))))) <=> (~r(z, s(elem!1)))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7719])).
% 1.85/2.05 tff(7721,plain,
% 1.85/2.05 (~r(z, s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7717, 7720])).
% 1.85/2.05 tff(7722,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1342, 7721])).
% 1.85/2.05 tff(7723,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | r(z, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(7724,plain,
% 1.85/2.05 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7723, 7717, 1342])).
% 1.85/2.05 tff(7725,plain,
% 1.85/2.05 (b(z, s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1992, 7717])).
% 1.85/2.05 tff(7726,plain,
% 1.85/2.05 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[353, 5568, 11])).
% 1.85/2.05 tff(7727,plain,
% 1.85/2.05 (~r(s(s(s(elem!1))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4553, 141, 7726, 1342])).
% 1.85/2.05 tff(7728,plain,
% 1.85/2.05 (b(s(s(s(elem!1))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[37, 7727])).
% 1.85/2.05 tff(7729,plain,
% 1.85/2.05 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4533, 7728, 1, 4105, 4186, 2562])).
% 1.85/2.05 tff(7730,plain,
% 1.85/2.05 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2558, 7729])).
% 1.85/2.05 tff(7731,plain,
% 1.85/2.05 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4959, 7730, 1097])).
% 1.85/2.05 tff(7732,plain,
% 1.85/2.05 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1263, 7731, 1])).
% 1.85/2.05 tff(7733,plain,
% 1.85/2.05 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1350, 7730, 1342])).
% 1.85/2.05 tff(7734,plain,
% 1.85/2.05 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[420, 7733, 7])).
% 1.85/2.05 tff(7735,plain,
% 1.85/2.05 (~(elem!1 = s(elem!1))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[169, 1961])).
% 1.85/2.05 tff(7736,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7737,plain,
% 1.85/2.05 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(7738,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[7737])).
% 1.85/2.05 tff(7739,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[7738, 7736])).
% 1.85/2.05 tff(7740,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(7741,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[7740, 7739])).
% 1.85/2.05 tff(7742,plain,
% 1.85/2.05 (~b(elem!1, s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7741, 245, 4105, 4186, 7728])).
% 1.85/2.05 tff(7743,plain,
% 1.85/2.05 (r(elem!1, s(s(s(elem!1))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1724, 7742, 1673])).
% 1.85/2.05 tff(7744,plain,
% 1.85/2.05 (~r(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2762, 7743, 7726])).
% 1.85/2.05 tff(7745,plain,
% 1.85/2.05 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[1086, 32, 7744])).
% 1.85/2.05 tff(7746,plain,
% 1.85/2.05 (b(elem!1, s(elem!1))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[7745, 7735])).
% 1.85/2.06 tff(7747,plain,
% 1.85/2.06 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3866, 7746, 7734, 7732])).
% 1.85/2.06 tff(7748,plain,
% 1.85/2.06 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[151, 7747, 2562])).
% 1.85/2.06 tff(7749,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1257, 305, 130, 1])).
% 1.85/2.06 tff(7750,plain,
% 1.85/2.06 (~b(z, s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4136, 245, 4105, 4186, 7749])).
% 1.85/2.06 tff(7751,plain,
% 1.85/2.06 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[559, 305, 556])).
% 1.85/2.06 tff(7752,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[353, 7751, 5568])).
% 1.85/2.06 tff(7753,plain,
% 1.85/2.06 (~r(z, s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2416, 141, 7752, 1342])).
% 1.85/2.06 tff(7754,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[197, 7753, 7750])).
% 1.85/2.06 tff(7755,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | b(s(s(s(elem!1))), s(elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(7756,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7755, 7748, 4105, 4186, 1342, 5568, 7732, 1])).
% 1.85/2.06 tff(7757,plain,
% 1.85/2.06 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2756, 7748, 7743])).
% 1.85/2.06 tff(7758,plain,
% 1.85/2.06 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1320, 7757, 2035])).
% 1.85/2.06 tff(7759,plain,
% 1.85/2.06 (~r(z, s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2416, 141, 7726, 1342])).
% 1.85/2.06 tff(7760,plain,
% 1.85/2.06 (b(z, s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[197, 7759])).
% 1.85/2.06 tff(7761,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7762,plain,
% 1.85/2.06 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, 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(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7763,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7762])).
% 1.85/2.06 tff(7764,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[7763, 7761])).
% 1.85/2.06 tff(7765,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(7766,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[7765, 7764])).
% 1.85/2.06 tff(7767,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7766, 245, 7760, 2197, 7758, 7756])).
% 1.85/2.06 tff(7768,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(7769,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7768, 7725, 4105, 4186, 1342, 7724, 2562, 169, 1097, 11])).
% 1.85/2.06 tff(7770,plain,
% 1.85/2.06 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[420, 1351, 7])).
% 1.85/2.06 tff(7771,plain,
% 1.85/2.06 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4959, 106, 1097])).
% 1.85/2.06 tff(7772,plain,
% 1.85/2.06 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1263, 7771, 1])).
% 1.85/2.06 tff(7773,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1295, 7772, 1287, 7770])).
% 1.85/2.06 tff(7774,plain,
% 1.85/2.06 (~r(s(s(s(elem!1))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1363, 7772, 1309, 1287, 106, 7, 1342])).
% 1.85/2.06 tff(7775,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[37, 7774])).
% 1.85/2.06 tff(7776,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7777,plain,
% 1.85/2.06 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7778,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7777])).
% 1.85/2.06 tff(7779,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[7778, 7776])).
% 1.85/2.06 tff(7780,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(7781,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[7780, 7779])).
% 1.85/2.06 tff(7782,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7781, 245, 4186, 1287, 7775, 2197, 7770])).
% 1.85/2.06 tff(7783,plain,
% 1.85/2.06 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1257, 7782, 1, 7773])).
% 1.85/2.06 tff(7784,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1239, 7773, 1309])).
% 1.85/2.06 tff(7785,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[110, 7782, 96])).
% 1.85/2.06 tff(7786,plain,
% 1.85/2.06 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[3538, 7785, 7784])).
% 1.85/2.06 tff(7787,assumption,(~r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.06 tff(7788,plain,
% 1.85/2.06 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1432, 399, 7787])).
% 1.85/2.06 tff(7789,assumption,(~r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.85/2.06 tff(7790,plain,
% 1.85/2.06 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[401, 399])).
% 1.85/2.06 tff(7791,plain,
% 1.85/2.06 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[151, 7790, 7789])).
% 1.85/2.06 tff(7792,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7667, 7791, 7788, 308, 556])).
% 1.85/2.06 tff(7793,plain,((elem!1 = s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), elem!1) | r(elem!1, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(7794,plain,
% 1.85/2.06 (elem!1 = s(s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7793, 7786, 308, 7772, 7783])).
% 1.85/2.06 tff(7795,plain,
% 1.85/2.06 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[151, 7783, 2562])).
% 1.85/2.06 tff(7796,plain,
% 1.85/2.06 (~b(elem!1, s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7334, 7795, 7770, 308])).
% 1.85/2.06 tff(7797,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[428, 7796, 7794, 7770])).
% 1.85/2.06 tff(7798,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(7799,plain,
% 1.85/2.06 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7798, 7724, 2562, 308, 4186, 7769, 7725, 2014, 1342, 1097])).
% 1.85/2.06 tff(7800,plain,
% 1.85/2.06 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2558, 7799])).
% 1.85/2.06 tff(7801,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4533, 7800, 7724, 4105, 4186, 2562])).
% 1.85/2.06 tff(7802,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[37, 7801])).
% 1.85/2.06 tff(7803,plain,
% 1.85/2.06 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4414, 141, 1097, 7802])).
% 1.85/2.06 tff(7804,plain,
% 1.85/2.06 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2091, 32, 7803])).
% 1.85/2.06 tff(7805,plain,
% 1.85/2.06 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7804, 2081])).
% 1.85/2.06 tff(7806,plain,
% 1.85/2.06 (~r(s(z), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4426, 7805, 7769, 9, 1097, 7802])).
% 1.85/2.06 tff(7807,plain,
% 1.85/2.06 (b(s(z), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[232, 7806])).
% 1.85/2.06 tff(7808,plain,
% 1.85/2.06 (~b(elem!1, s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4214, 245, 4105, 4186, 7807])).
% 1.85/2.06 tff(7809,plain,
% 1.85/2.06 (~(s(s(s(elem!1))) = elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[95, 7724])).
% 1.85/2.06 tff(7810,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7811,plain,
% 1.85/2.06 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7812,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7811])).
% 1.85/2.06 tff(7813,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.85/2.06 inference(transitivity,[status(thm)],[7812, 7810])).
% 1.85/2.06 tff(7814,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(7815,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[7814, 7813])).
% 1.85/2.06 tff(7816,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7815, 245, 4105, 4186, 308, 2939, 1427])).
% 1.85/2.06 tff(7817,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(7818,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7817, 7805, 4186, 308, 4105])).
% 1.85/2.06 tff(7819,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[110, 7818, 7809])).
% 1.85/2.06 tff(7820,plain,
% 1.85/2.06 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4511, 245, 4105, 4186, 7800])).
% 1.85/2.06 tff(7821,plain,
% 1.85/2.06 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[151, 7820, 2562])).
% 1.85/2.06 tff(7822,plain,
% 1.85/2.06 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1257, 7818, 7724, 7821])).
% 1.85/2.06 tff(7823,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7824,plain,
% 1.85/2.06 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7825,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7824])).
% 1.85/2.06 tff(7826,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[7825, 7823])).
% 1.85/2.06 tff(7827,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~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))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(7828,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[7827, 7826])).
% 1.85/2.06 tff(7829,plain,
% 1.85/2.06 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7828, 245, 4105, 308, 7805, 7822, 7800])).
% 1.85/2.06 tff(7830,plain,
% 1.85/2.06 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1263, 7829, 7724])).
% 1.85/2.06 tff(7831,plain,
% 1.85/2.06 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4959, 1366, 1097])).
% 1.85/2.06 tff(7832,plain,
% 1.85/2.06 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2558, 7831])).
% 1.85/2.06 tff(7833,plain,
% 1.85/2.06 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4458, 245, 4105, 4186, 355, 7832])).
% 1.85/2.06 tff(7834,plain,
% 1.85/2.06 ((s(z) = s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[2448, 32, 7833])).
% 1.85/2.06 tff(7835,plain,
% 1.85/2.06 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7834, 2438])).
% 1.85/2.06 tff(7836,plain,
% 1.85/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), 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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7837,plain,
% 1.85/2.06 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7838,plain,
% 1.85/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7837])).
% 1.85/2.06 tff(7839,plain,
% 1.85/2.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(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(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[7838, 7836])).
% 1.85/2.06 tff(7840,plain,
% 1.85/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(7841,plain,
% 1.85/2.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[7840, 7839])).
% 1.85/2.06 tff(7842,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7841, 141, 486, 1366, 7835])).
% 1.85/2.06 tff(7843,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(7844,plain,
% 1.85/2.06 (~r(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7843, 7830, 4105, 4186, 7807, 1097])).
% 1.85/2.06 tff(7845,plain,
% 1.85/2.06 (b(s(z), s(elem!1))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[440, 7844, 9])).
% 1.85/2.06 tff(7846,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7847,plain,
% 1.85/2.06 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(7848,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7847])).
% 1.85/2.06 tff(7849,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[7848, 7846])).
% 1.85/2.06 tff(7850,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(7851,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[7850, 7849])).
% 1.85/2.06 tff(7852,plain,
% 1.85/2.06 (~b(s(s(s(elem!1))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[7851, 245, 7769, 7805, 7845])).
% 1.85/2.06 tff(7853,plain,
% 1.85/2.06 (r(s(s(s(elem!1))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[265, 7852])).
% 1.85/2.06 tff(7854,plain,
% 1.85/2.06 (~r(elem!1, s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[276, 7853, 7819])).
% 1.85/2.06 tff(7855,plain,
% 1.85/2.06 (elem!1 = s(z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[281, 7854, 7808])).
% 1.85/2.06 tff(7856,plain,
% 1.85/2.06 (s(elem!1) = s(s(z))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7855])).
% 1.85/2.06 tff(7857,plain,
% 1.85/2.06 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7856])).
% 1.85/2.06 tff(7858,plain,
% 1.85/2.06 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7857])).
% 1.85/2.06 tff(7859,plain,
% 1.85/2.06 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7858])).
% 1.85/2.06 tff(7860,plain,
% 1.85/2.06 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.85/2.06 inference(symmetry,[status(thm)],[7859])).
% 1.85/2.06 tff(7861,plain,
% 1.85/2.06 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[7860])).
% 1.85/2.06 tff(7862,plain,
% 1.85/2.06 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.85/2.06 inference(symmetry,[status(thm)],[7861])).
% 1.85/2.06 tff(7863,plain,
% 1.85/2.06 (s(s(z)) = s(elem!1)),
% 1.85/2.06 inference(symmetry,[status(thm)],[7856])).
% 1.85/2.06 tff(7864,plain,
% 1.85/2.06 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7863])).
% 1.85/2.07 tff(7865,plain,
% 1.85/2.07 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.85/2.07 inference(symmetry,[status(thm)],[7864])).
% 1.85/2.07 tff(7866,plain,
% 1.85/2.07 (r(s(s(z)), z)),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[1097, 7865])).
% 1.85/2.07 tff(7867,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7855])).
% 1.85/2.07 tff(7868,plain,
% 1.85/2.07 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2156, 7724, 7855])).
% 1.85/2.07 tff(7869,plain,
% 1.85/2.07 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2163, 7868])).
% 1.85/2.07 tff(7870,plain,
% 1.85/2.07 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4414, 141, 1097, 1355])).
% 1.85/2.07 tff(7871,plain,
% 1.85/2.07 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2091, 32, 7870])).
% 1.85/2.07 tff(7872,plain,
% 1.85/2.07 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7871, 2081])).
% 1.85/2.07 tff(7873,plain,
% 1.85/2.07 (~r(s(z), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4426, 7872, 1287, 9, 1097, 1355])).
% 1.85/2.07 tff(7874,plain,
% 1.85/2.07 (b(s(z), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[232, 7873])).
% 1.85/2.07 tff(7875,plain,
% 1.85/2.07 (~b(elem!1, s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4214, 245, 4105, 4186, 355])).
% 1.85/2.07 tff(7876,plain,
% 1.85/2.07 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7817, 2939, 4186, 308, 4105])).
% 1.85/2.07 tff(7877,plain,
% 1.85/2.07 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[110, 7876, 96])).
% 1.85/2.07 tff(7878,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1257, 4513, 1, 7876])).
% 1.85/2.07 tff(7879,plain,
% 1.85/2.07 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7828, 245, 4105, 308, 2939, 7878, 1943])).
% 1.85/2.07 tff(7880,plain,
% 1.85/2.07 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1263, 7879, 1])).
% 1.85/2.07 tff(7881,plain,
% 1.85/2.07 (~r(s(z), s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7843, 7880, 4105, 4186, 355, 1097])).
% 1.85/2.07 tff(7882,plain,
% 1.85/2.07 (b(s(z), s(elem!1))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[440, 7881, 9])).
% 1.85/2.07 tff(7883,plain,
% 1.85/2.07 (~b(s(s(s(elem!1))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7851, 245, 1287, 2939, 7882])).
% 1.85/2.07 tff(7884,plain,
% 1.85/2.07 (r(s(s(s(elem!1))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[265, 7883])).
% 1.85/2.07 tff(7885,plain,
% 1.85/2.07 (~r(elem!1, s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[276, 7884, 7877])).
% 1.85/2.07 tff(7886,plain,
% 1.85/2.07 (elem!1 = s(z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[281, 7885, 7875])).
% 1.85/2.07 tff(7887,plain,
% 1.85/2.07 (s(elem!1) = s(s(z))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7886])).
% 1.85/2.07 tff(7888,plain,
% 1.85/2.07 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7887])).
% 1.85/2.07 tff(7889,plain,
% 1.85/2.07 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7888])).
% 1.85/2.07 tff(7890,plain,
% 1.85/2.07 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.85/2.07 inference(symmetry,[status(thm)],[7889])).
% 1.85/2.07 tff(7891,plain,
% 1.85/2.07 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7889])).
% 1.85/2.07 tff(7892,plain,
% 1.85/2.07 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[7891])).
% 1.85/2.07 tff(7893,plain,
% 1.85/2.07 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7892, 7890])).
% 1.85/2.07 tff(7894,plain,
% 1.85/2.07 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[7893])).
% 1.85/2.07 tff(7895,plain,
% 1.85/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1315, 141, 7877, 4513])).
% 1.85/2.07 tff(7896,plain,
% 1.85/2.07 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1320, 7895, 1487])).
% 1.85/2.07 tff(7897,plain,
% 1.85/2.07 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7896, 7894])).
% 1.85/2.07 tff(7898,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7890])).
% 1.85/2.07 tff(7899,plain,
% 1.85/2.07 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.85/2.07 inference(symmetry,[status(thm)],[7898])).
% 1.85/2.07 tff(7900,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7884, 7899])).
% 1.85/2.07 tff(7901,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7886])).
% 1.85/2.07 tff(7902,plain,
% 1.85/2.07 ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7901])).
% 1.85/2.07 tff(7903,plain,
% 1.85/2.07 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[3905, 7902])).
% 1.85/2.07 tff(7904,plain,
% 1.85/2.07 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1820, 7903])).
% 1.85/2.07 tff(7905,plain,
% 1.85/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7906,plain,
% 1.85/2.07 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7907,plain,
% 1.85/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(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(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7906])).
% 1.85/2.07 tff(7908,plain,
% 1.85/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(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(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[7907, 7905])).
% 1.85/2.07 tff(7909,plain,
% 1.85/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(7910,plain,
% 1.85/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7909, 7908])).
% 1.85/2.07 tff(7911,plain,
% 1.85/2.07 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7910, 141, 7904])).
% 1.85/2.07 tff(7912,plain,
% 1.85/2.07 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7911, 7900])).
% 1.85/2.07 tff(7913,plain,
% 1.85/2.07 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4324, 32, 2912, 7912])).
% 1.85/2.07 tff(7914,plain,
% 1.85/2.07 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7890, 7892])).
% 1.85/2.07 tff(7915,plain,
% 1.85/2.07 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[7914])).
% 1.85/2.07 tff(7916,plain,
% 1.85/2.07 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7878, 7915])).
% 1.85/2.07 tff(7917,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7892])).
% 1.85/2.07 tff(7918,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[7917])).
% 1.85/2.07 tff(7919,plain,
% 1.85/2.07 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7892])).
% 1.85/2.07 tff(7920,plain,
% 1.85/2.07 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7919])).
% 1.85/2.07 tff(7921,plain,
% 1.85/2.07 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7891])).
% 1.85/2.07 tff(7922,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7923,plain,
% 1.85/2.07 (((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7924,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7923])).
% 1.85/2.07 tff(7925,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[7924, 7922])).
% 1.85/2.07 tff(7926,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(7927,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7926, 7925])).
% 1.85/2.07 tff(7928,plain,
% 1.85/2.07 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7927, 245, 4105, 4186, 355, 1943])).
% 1.85/2.07 tff(7929,plain,
% 1.85/2.07 (r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[217, 7928])).
% 1.85/2.07 tff(7930,plain,
% 1.85/2.07 (r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7929, 7921])).
% 1.85/2.07 tff(7931,plain,
% 1.85/2.07 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2206, 141, 7904, 7930])).
% 1.85/2.07 tff(7932,plain,
% 1.85/2.07 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7931, 7920])).
% 1.85/2.07 tff(7933,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[501, 7932, 2193])).
% 1.85/2.07 tff(7934,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7933, 7918])).
% 1.85/2.07 tff(7935,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7936,plain,
% 1.85/2.07 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7937,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7936])).
% 1.85/2.07 tff(7938,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[7937, 7935])).
% 1.85/2.07 tff(7939,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(7940,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7939, 7938])).
% 1.85/2.07 tff(7941,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7940, 245, 7934, 7916, 7913, 7897])).
% 1.85/2.07 tff(7942,plain,((~b(s(s(s(s(elem!1)))), z)) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~r(s(elem!1), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(7943,plain,
% 1.85/2.07 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7942, 7872, 332, 3905, 1287, 2912, 9, 4105, 4186, 7874, 1097, 2035, 1, 308, 2562])).
% 1.85/2.07 tff(7944,plain,
% 1.85/2.07 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2558, 7943])).
% 1.85/2.07 tff(7945,plain,
% 1.85/2.07 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4959, 7944, 1097])).
% 1.85/2.07 tff(7946,plain,
% 1.85/2.07 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1363, 7944, 2014, 1287, 1355, 7, 1342])).
% 1.85/2.07 tff(7947,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1263, 7946, 7945, 1])).
% 1.85/2.07 tff(7948,plain,((~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(elem!1), z)) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(7949,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7948, 7869, 7769, 1342, 1097, 7802, 7724, 9, 4105, 4186, 308, 2562, 11])).
% 1.85/2.07 tff(7950,plain,
% 1.85/2.07 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7949, 7867])).
% 1.85/2.07 tff(7951,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7952,plain,
% 1.85/2.07 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7953,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7952])).
% 1.85/2.07 tff(7954,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[7953, 7951])).
% 1.85/2.07 tff(7955,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(7956,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[7955, 7954])).
% 1.85/2.07 tff(7957,plain,
% 1.85/2.07 (~b(z, s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[7956, 245, 4105, 7725, 7822, 7800])).
% 1.85/2.07 tff(7958,plain,
% 1.85/2.07 (r(z, s(s(s(elem!1))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[197, 7957])).
% 1.85/2.07 tff(7959,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7960,plain,
% 1.85/2.07 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(7961,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[7960])).
% 1.85/2.07 tff(7962,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[7961, 7959])).
% 1.85/2.08 tff(7963,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(7964,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[7963, 7962])).
% 1.85/2.08 tff(7965,plain,
% 1.85/2.08 ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7964, 245, 7805, 7807, 7822, 7800])).
% 1.85/2.08 tff(7966,plain,
% 1.85/2.08 (~b(s(z), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7965, 7845])).
% 1.85/2.08 tff(7967,plain,
% 1.85/2.08 (r(s(z), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1133, 7966])).
% 1.85/2.08 tff(7968,plain,
% 1.85/2.08 (~r(z, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6558, 141, 7967, 7958])).
% 1.85/2.08 tff(7969,plain,
% 1.85/2.08 (b(z, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1421, 7968])).
% 1.85/2.08 tff(7970,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(7971,plain,
% 1.85/2.08 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(7972,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[7971])).
% 1.85/2.08 tff(7973,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[7972, 7970])).
% 1.85/2.08 tff(7974,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(7975,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[7974, 7973])).
% 1.85/2.08 tff(7976,plain,
% 1.85/2.08 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7975, 245, 7807, 7969, 7950])).
% 1.85/2.08 tff(7977,plain,
% 1.85/2.08 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2220, 32, 1554, 7976])).
% 1.85/2.08 tff(7978,plain,
% 1.85/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(7979,plain,
% 1.85/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(7980,plain,
% 1.85/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[7979, 7978])).
% 1.85/2.08 tff(7981,plain,
% 1.85/2.08 ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7980, 141, 7977])).
% 1.85/2.08 tff(7982,plain,
% 1.85/2.08 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7981, 7866])).
% 1.85/2.08 tff(7983,plain,
% 1.85/2.08 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[7863])).
% 1.85/2.08 tff(7984,plain,
% 1.85/2.08 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[7983])).
% 1.85/2.08 tff(7985,plain,
% 1.85/2.08 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[7855])).
% 1.85/2.08 tff(7986,plain,
% 1.85/2.08 (b(s(elem!1), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[308, 7985])).
% 1.85/2.08 tff(7987,plain,
% 1.85/2.08 (b(s(s(z)), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[7986, 7984])).
% 1.85/2.08 tff(7988,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(7989,plain,
% 1.85/2.08 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(7990,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[7989])).
% 1.85/2.08 tff(7991,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[7990, 7988])).
% 1.85/2.08 tff(7992,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(7993,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[7992, 7991])).
% 1.85/2.08 tff(7994,plain,
% 1.85/2.08 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7993, 245, 7807, 7987, 7969, 7950])).
% 1.85/2.08 tff(7995,plain,
% 1.85/2.08 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2270, 32, 7994])).
% 1.85/2.08 tff(7996,plain,
% 1.85/2.08 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7995, 7982])).
% 1.85/2.08 tff(7997,plain,
% 1.85/2.08 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(z)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[7996])).
% 1.85/2.08 tff(7998,plain,
% 1.85/2.08 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[7997])).
% 1.85/2.08 tff(7999,plain,
% 1.85/2.08 (s(z) = s(s(s(s(s(s(z))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[591, 7998, 320, 7862])).
% 1.85/2.08 tff(8000,plain,
% 1.85/2.08 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[7999])).
% 1.85/2.08 tff(8001,plain,
% 1.85/2.08 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[8000])).
% 1.85/2.08 tff(8002,plain,
% 1.85/2.08 (s(s(s(s(s(z))))) = z),
% 1.85/2.08 inference(transitivity,[status(thm)],[2278, 8001, 52])).
% 1.85/2.08 tff(8003,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[734, 8002])).
% 1.85/2.08 tff(8004,plain,(r(z, s(s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(elem!1))) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(8005,plain,
% 1.85/2.08 (r(z, s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[8004, 1097, 1342, 9, 4105, 4186, 308, 2562, 11, 169])).
% 1.85/2.08 tff(8006,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1239, 305, 1309])).
% 1.85/2.08 tff(8007,plain,
% 1.85/2.08 (~r(s(s(s(elem!1))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3336, 141, 310, 8006])).
% 1.85/2.08 tff(8008,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[37, 8007])).
% 1.85/2.08 tff(8009,plain,
% 1.85/2.08 (~r(z, s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3358, 141, 310, 8006])).
% 1.85/2.08 tff(8010,plain,
% 1.85/2.08 (b(z, s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[197, 8009])).
% 1.85/2.08 tff(8011,plain,
% 1.85/2.08 (~b(s(s(s(elem!1))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4562, 8010, 4186, 8008])).
% 1.85/2.08 tff(8012,plain,
% 1.85/2.08 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1257, 8011, 1, 305])).
% 1.85/2.08 tff(8013,plain,
% 1.85/2.08 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[2562, 1942])).
% 1.85/2.08 tff(8014,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[110, 8011, 96])).
% 1.85/2.08 tff(8015,plain,
% 1.85/2.08 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3538, 8014, 8006])).
% 1.85/2.08 tff(8016,plain,
% 1.85/2.08 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4533, 8008, 1, 4105, 4186, 2562])).
% 1.85/2.08 tff(8017,plain,
% 1.85/2.08 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2558, 8016])).
% 1.85/2.08 tff(8018,plain,
% 1.85/2.08 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4959, 8017, 1097])).
% 1.85/2.08 tff(8019,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1263, 8018, 1])).
% 1.85/2.08 tff(8020,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7793, 8019, 8015, 308, 8013, 8012])).
% 1.85/2.08 tff(8021,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(8022,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[8021, 1, 308, 1097, 4186, 4105, 2562, 8005, 2014])).
% 1.85/2.08 tff(8023,plain,
% 1.85/2.08 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3674, 8005, 1342])).
% 1.85/2.08 tff(8024,plain,
% 1.85/2.08 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[420, 7, 8023])).
% 1.85/2.08 tff(8025,plain,
% 1.85/2.08 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5306, 1097, 8005])).
% 1.85/2.08 tff(8026,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1263, 1, 8025])).
% 1.85/2.08 tff(8027,plain,
% 1.85/2.08 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1295, 8026, 8024, 8022])).
% 1.85/2.08 tff(8028,plain,
% 1.85/2.08 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4533, 4555, 1, 4105, 4186, 2562])).
% 1.85/2.08 tff(8029,plain,
% 1.85/2.08 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2558, 8028])).
% 1.85/2.08 tff(8030,plain,
% 1.85/2.08 (~b(elem!1, s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7741, 245, 4105, 4186, 4555])).
% 1.85/2.08 tff(8031,plain,
% 1.85/2.08 (r(elem!1, s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1724, 8030, 1673])).
% 1.85/2.08 tff(8032,plain,
% 1.85/2.08 (~r(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2762, 8031, 371])).
% 1.85/2.08 tff(8033,plain,
% 1.85/2.08 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1086, 32, 8032])).
% 1.85/2.08 tff(8034,plain,
% 1.85/2.08 (b(elem!1, s(elem!1))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[8033, 7735])).
% 1.85/2.08 tff(8035,plain,
% 1.85/2.08 (~r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1111, 8034, 308, 10, 9, 8029, 1097])).
% 1.85/2.08 tff(8036,plain,
% 1.85/2.08 (b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[232, 8035])).
% 1.85/2.08 tff(8037,plain,
% 1.85/2.08 (~b(elem!1, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4214, 245, 4105, 4186, 8036])).
% 1.85/2.08 tff(8038,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[110, 4563, 96])).
% 1.85/2.08 tff(8039,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(8040,plain,
% 1.85/2.08 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(8041,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8040])).
% 1.85/2.08 tff(8042,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[8041, 8039])).
% 1.85/2.08 tff(8043,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(8044,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[8043, 8042])).
% 1.85/2.08 tff(8045,plain,
% 1.85/2.08 (~b(s(s(s(elem!1))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[8044, 245, 4105, 4186, 4555, 8036])).
% 1.85/2.08 tff(8046,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[265, 8045])).
% 1.85/2.08 tff(8047,plain,
% 1.85/2.08 (~r(elem!1, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[276, 8046, 8038])).
% 1.85/2.08 tff(8048,plain,
% 1.85/2.08 (elem!1 = s(z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[281, 8047, 8037])).
% 1.85/2.08 tff(8049,plain,
% 1.85/2.08 (s(elem!1) = s(s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8048])).
% 1.85/2.08 tff(8050,plain,
% 1.85/2.08 (s(s(elem!1)) = s(s(s(z)))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8049])).
% 1.85/2.08 tff(8051,plain,
% 1.85/2.08 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8050])).
% 1.85/2.08 tff(8052,plain,
% 1.85/2.08 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8051])).
% 1.85/2.08 tff(8053,plain,
% 1.85/2.08 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[8052])).
% 1.85/2.08 tff(8054,plain,
% 1.85/2.08 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8053])).
% 1.85/2.08 tff(8055,plain,
% 1.85/2.08 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[8054])).
% 1.85/2.08 tff(8056,plain,
% 1.85/2.08 (s(s(z)) = s(elem!1)),
% 1.85/2.08 inference(symmetry,[status(thm)],[8049])).
% 1.85/2.08 tff(8057,plain,
% 1.85/2.08 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8056])).
% 1.85/2.08 tff(8058,plain,
% 1.85/2.08 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.85/2.08 inference(symmetry,[status(thm)],[8057])).
% 1.85/2.08 tff(8059,plain,
% 1.85/2.08 (r(s(s(z)), z)),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[1097, 8058])).
% 1.85/2.08 tff(8060,plain,
% 1.85/2.08 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8052])).
% 1.85/2.08 tff(8061,plain,
% 1.85/2.08 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4959, 8029, 1097])).
% 1.85/2.08 tff(8062,plain,
% 1.85/2.08 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1263, 8061, 1])).
% 1.85/2.08 tff(8063,plain,
% 1.85/2.08 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3866, 8034, 10, 8062])).
% 1.85/2.08 tff(8064,plain,
% 1.85/2.08 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4262, 8048, 8063])).
% 1.85/2.08 tff(8065,plain,
% 1.85/2.08 (r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[217, 8064])).
% 1.85/2.08 tff(8066,plain,
% 1.85/2.08 (r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[8065, 8060])).
% 1.85/2.08 tff(8067,plain,
% 1.85/2.08 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2156, 8048, 1])).
% 1.85/2.08 tff(8068,plain,
% 1.85/2.08 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2163, 8067])).
% 1.85/2.08 tff(8069,plain,
% 1.85/2.08 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[151, 8063, 2562])).
% 1.85/2.08 tff(8070,plain,
% 1.85/2.08 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2756, 8069, 8031])).
% 1.85/2.08 tff(8071,plain,
% 1.85/2.08 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1320, 8070, 3067])).
% 1.85/2.08 tff(8072,plain,
% 1.85/2.08 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2395, 8034, 8013, 371, 8031, 1])).
% 1.85/2.08 tff(8073,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1239, 8072, 1309])).
% 1.85/2.08 tff(8074,plain,
% 1.85/2.08 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.85/2.08 inference(symmetry,[status(thm)],[2141])).
% 1.85/2.08 tff(8075,plain,
% 1.85/2.08 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8074])).
% 1.85/2.08 tff(8076,plain,
% 1.85/2.08 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[8075])).
% 1.85/2.08 tff(8077,plain,
% 1.85/2.08 (r(s(s(s(s(z)))), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[267, 8076])).
% 1.85/2.08 tff(8078,plain,
% 1.85/2.08 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7910, 141, 2203])).
% 1.85/2.08 tff(8079,plain,
% 1.85/2.08 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[8078, 8077])).
% 1.85/2.08 tff(8080,plain,
% 1.85/2.08 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4324, 32, 2912, 8079])).
% 1.85/2.08 tff(8081,plain,
% 1.85/2.08 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8074, 2143])).
% 1.85/2.08 tff(8082,plain,
% 1.85/2.08 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[8081])).
% 1.85/2.08 tff(8083,plain,
% 1.85/2.08 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[1276, 8082])).
% 1.85/2.08 tff(8084,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[2143, 8074])).
% 1.85/2.08 tff(8085,plain,
% 1.85/2.08 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.08 inference(symmetry,[status(thm)],[8084])).
% 1.85/2.08 tff(8086,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[1528, 8085])).
% 1.85/2.08 tff(8087,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7940, 245, 8086, 2210, 8083, 8080])).
% 1.85/2.08 tff(8088,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(8089,plain,
% 1.85/2.08 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[8088, 8073, 8048, 8071, 8068, 2193, 8046, 8066])).
% 1.85/2.08 tff(8090,plain,
% 1.85/2.08 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1820, 8089])).
% 1.85/2.08 tff(8091,plain,
% 1.85/2.08 (~r(z, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4226, 8065, 8029])).
% 1.85/2.08 tff(8092,plain,
% 1.85/2.08 (b(z, s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[1421, 8091])).
% 1.85/2.08 tff(8093,plain,
% 1.85/2.08 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7975, 245, 8036, 8092, 8090])).
% 1.85/2.08 tff(8094,plain,
% 1.85/2.08 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2220, 32, 1554, 8093])).
% 1.85/2.08 tff(8095,plain,
% 1.85/2.08 ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7980, 141, 8094])).
% 1.85/2.08 tff(8096,plain,
% 1.85/2.08 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[8095, 8059])).
% 1.85/2.08 tff(8097,plain,
% 1.85/2.08 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8056])).
% 1.85/2.08 tff(8098,plain,
% 1.85/2.08 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.85/2.08 inference(symmetry,[status(thm)],[8097])).
% 1.85/2.08 tff(8099,plain,
% 1.85/2.08 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[8048])).
% 1.85/2.08 tff(8100,plain,
% 1.85/2.08 (b(s(elem!1), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[308, 8099])).
% 1.85/2.08 tff(8101,plain,
% 1.85/2.08 (b(s(s(z)), s(z))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[8100, 8098])).
% 1.85/2.08 tff(8102,plain,
% 1.85/2.08 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[7993, 245, 8036, 8101, 8092, 8090])).
% 1.85/2.09 tff(8103,plain,
% 1.85/2.09 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2270, 32, 8102])).
% 1.85/2.09 tff(8104,plain,
% 1.85/2.09 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8103, 8096])).
% 1.85/2.09 tff(8105,plain,
% 1.85/2.09 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(z)))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8104])).
% 1.85/2.09 tff(8106,plain,
% 1.85/2.09 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(symmetry,[status(thm)],[8105])).
% 1.85/2.09 tff(8107,plain,
% 1.85/2.09 (s(z) = s(s(s(s(s(s(z))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[591, 8106, 320, 8055])).
% 1.85/2.09 tff(8108,plain,
% 1.85/2.09 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8107])).
% 1.85/2.09 tff(8109,plain,
% 1.85/2.09 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.85/2.09 inference(symmetry,[status(thm)],[8108])).
% 1.85/2.09 tff(8110,plain,
% 1.85/2.09 (s(s(s(s(s(z))))) = z),
% 1.85/2.09 inference(transitivity,[status(thm)],[2278, 8109, 52])).
% 1.85/2.09 tff(8111,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[734, 8110])).
% 1.85/2.09 tff(8112,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = elem!1) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8113,plain,
% 1.85/2.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8112, 8024, 332, 308, 1097, 4105, 4186, 1, 9, 2014, 2562, 169, 1342])).
% 1.85/2.09 tff(8114,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[353, 8113, 8027, 11])).
% 1.85/2.09 tff(8115,plain,((s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (s(elem!1) = elem!1) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8116,plain,
% 1.85/2.09 (~r(s(elem!1), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8115, 7716, 1, 4105, 11, 4186, 9, 2562, 105, 308])).
% 1.85/2.09 tff(8117,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[653, 32, 638, 8116, 7708])).
% 1.85/2.09 tff(8118,plain,((~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8119,plain,
% 1.85/2.09 (s(s(s(s(elem!1)))) = elem!1),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8118, 11, 7316, 4186, 1, 9, 7699])).
% 1.85/2.09 tff(8120,plain,
% 1.85/2.09 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1051, 8119])).
% 1.85/2.09 tff(8121,plain,
% 1.85/2.09 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[775, 8120])).
% 1.85/2.09 tff(8122,plain,
% 1.85/2.09 (s(s(s(elem!1))) = s(elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[7113, 1939])).
% 1.85/2.09 tff(8123,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[11, 8122])).
% 1.85/2.09 tff(8124,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8125,plain,
% 1.85/2.09 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8124, 11])).
% 1.85/2.09 tff(8126,plain,
% 1.85/2.09 (~b(s(elem!1), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[7707, 7699, 7316, 4186])).
% 1.85/2.09 tff(8127,plain,
% 1.85/2.09 (r(s(elem!1), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1039, 8126])).
% 1.85/2.09 tff(8128,plain,
% 1.85/2.09 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4414, 141, 8127, 1355])).
% 1.85/2.09 tff(8129,plain,
% 1.85/2.09 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2091, 32, 8128])).
% 1.85/2.09 tff(8130,plain,
% 1.85/2.09 (b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8129, 8125])).
% 1.85/2.09 tff(8131,plain,
% 1.85/2.09 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3654, 141, 8127, 1355])).
% 1.85/2.09 tff(8132,plain,
% 1.85/2.09 (b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[353, 11, 8131])).
% 1.85/2.09 tff(8133,plain,
% 1.85/2.09 (~r(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4426, 8132, 1355, 9, 8127, 8130])).
% 1.85/2.09 tff(8134,plain,
% 1.85/2.09 (b(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[232, 8133])).
% 1.85/2.09 tff(8135,plain,
% 1.85/2.09 (~b(s(z), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4436, 8134, 7699, 4186])).
% 1.85/2.09 tff(8136,plain,
% 1.85/2.09 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8119])).
% 1.85/2.09 tff(8137,plain,
% 1.85/2.09 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.85/2.09 inference(transitivity,[status(thm)],[8136, 339])).
% 1.85/2.09 tff(8138,plain,
% 1.85/2.09 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8137])).
% 1.85/2.09 tff(8139,plain,
% 1.85/2.09 (~(s(z) = elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[209, 8138])).
% 1.85/2.09 tff(8140,plain,
% 1.85/2.09 (r(s(z), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[389, 8139, 8135])).
% 1.85/2.09 tff(8141,plain,
% 1.85/2.09 (~r(s(z), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1143, 8140, 170])).
% 1.85/2.09 tff(8142,plain,
% 1.85/2.09 (b(s(z), s(s(s(elem!1))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1133, 8141])).
% 1.85/2.09 tff(8143,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8144,plain,
% 1.85/2.09 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8145,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8144])).
% 1.85/2.09 tff(8146,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[8145, 8143])).
% 1.85/2.09 tff(8147,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(8148,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8147, 8146])).
% 1.85/2.09 tff(8149,plain,
% 1.85/2.09 ((~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8148, 245, 4186, 8132, 7316, 8134])).
% 1.85/2.09 tff(8150,plain,
% 1.85/2.09 (~b(s(z), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8149, 8142])).
% 1.85/2.09 tff(8151,plain,
% 1.85/2.09 (r(s(z), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[440, 8150, 9])).
% 1.85/2.09 tff(8152,plain,
% 1.85/2.09 (~b(z, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[7714, 245, 7699, 4186, 7316])).
% 1.85/2.09 tff(8153,plain,
% 1.85/2.09 (r(z, s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[644, 8152])).
% 1.85/2.09 tff(8154,plain,
% 1.85/2.09 (~r(z, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2403, 141, 8153, 8151])).
% 1.85/2.09 tff(8155,plain,
% 1.85/2.09 (b(z, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1421, 8154])).
% 1.85/2.09 tff(8156,plain,
% 1.85/2.09 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8136])).
% 1.85/2.09 tff(8157,plain,
% 1.85/2.09 (~(elem!1 = s(z))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[209, 8156])).
% 1.85/2.09 tff(8158,plain,
% 1.85/2.09 (~b(elem!1, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4214, 245, 7699, 4186, 8134])).
% 1.85/2.09 tff(8159,plain,
% 1.85/2.09 (r(elem!1, s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[281, 8158, 8157])).
% 1.85/2.09 tff(8160,plain,
% 1.85/2.09 (~r(s(s(s(elem!1))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[276, 8159, 170])).
% 1.85/2.09 tff(8161,plain,
% 1.85/2.09 (b(s(s(s(elem!1))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[265, 8160])).
% 1.85/2.09 tff(8162,plain,
% 1.85/2.09 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[598])).
% 1.85/2.09 tff(8163,plain,
% 1.85/2.09 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(symmetry,[status(thm)],[8162])).
% 1.85/2.09 tff(8164,plain,
% 1.85/2.09 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8163])).
% 1.85/2.09 tff(8165,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8166,plain,
% 1.85/2.09 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8167,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8166])).
% 1.85/2.09 tff(8168,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[8167, 8165])).
% 1.85/2.09 tff(8169,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(8170,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8169, 8168])).
% 1.85/2.09 tff(8171,plain,
% 1.85/2.09 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8170, 245, 355, 7047, 4187, 6898])).
% 1.85/2.09 tff(8172,plain,
% 1.85/2.09 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8171, 8164])).
% 1.85/2.09 tff(8173,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.85/2.09 tff(8174,plain,
% 1.85/2.09 (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8173, 5913])).
% 1.85/2.09 tff(8175,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[673, 8174])).
% 1.85/2.09 tff(8176,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8177,plain,
% 1.85/2.09 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8176, 6873])).
% 1.85/2.09 tff(8178,plain,
% 1.85/2.09 (((~![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(z))))), elem!1)) | (~r(s(s(s(elem!1))), 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))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8179,plain,
% 1.85/2.09 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8180,plain,
% 1.85/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, 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(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8179])).
% 1.85/2.09 tff(8181,plain,
% 1.85/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, 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(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[8180, 8178])).
% 1.85/2.09 tff(8182,plain,
% 1.85/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(8183,plain,
% 1.85/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8182, 8181])).
% 1.85/2.09 tff(8184,plain,
% 1.85/2.09 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8183, 141, 170, 2628])).
% 1.85/2.09 tff(8185,plain,
% 1.85/2.09 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8184, 7078])).
% 1.85/2.09 tff(8186,plain,
% 1.85/2.09 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6009, 8185, 8177])).
% 1.85/2.09 tff(8187,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8186, 8172])).
% 1.85/2.09 tff(8188,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~(s(s(s(s(elem!1)))) = elem!1)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8189,plain,
% 1.85/2.09 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8188, 8119, 8134, 8161, 8155, 170, 8140])).
% 1.85/2.09 tff(8190,plain,
% 1.85/2.09 (b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[787, 8189, 8121])).
% 1.85/2.09 tff(8191,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8192,plain,
% 1.85/2.09 (((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8193,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8192])).
% 1.85/2.09 tff(8194,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[8193, 8191])).
% 1.85/2.09 tff(8195,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(8196,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8195, 8194])).
% 1.85/2.09 tff(8197,plain,
% 1.85/2.09 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8196, 245, 7699, 4186, 7316, 8190])).
% 1.85/2.09 tff(8198,plain,
% 1.85/2.09 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1065, 8119, 9])).
% 1.85/2.09 tff(8199,plain,
% 1.85/2.09 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5923, 8198])).
% 1.85/2.09 tff(8200,plain,
% 1.85/2.09 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5933, 32, 8199, 8197])).
% 1.85/2.09 tff(8201,plain,
% 1.85/2.09 (~b(s(s(s(s(s(z))))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6914, 245, 7699, 4186, 8190])).
% 1.85/2.09 tff(8202,plain,
% 1.85/2.09 (r(s(s(s(s(s(z))))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[738, 8201])).
% 1.85/2.09 tff(8203,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5929, 141, 8127, 8202, 8200])).
% 1.85/2.09 tff(8204,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8205,plain,
% 1.85/2.09 (s(s(s(elem!1))) = s(elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8204, 111, 4186, 9, 1355, 1])).
% 1.85/2.09 tff(8206,plain,
% 1.85/2.09 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8205])).
% 1.85/2.09 tff(8207,plain,
% 1.85/2.09 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.85/2.09 inference(symmetry,[status(thm)],[8206])).
% 1.85/2.09 tff(8208,plain,
% 1.85/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[7316, 8207])).
% 1.85/2.09 tff(8209,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[88, 8208])).
% 1.85/2.09 tff(8210,plain,(b(s(s(s(elem!1))), elem!1) | (~b(elem!1, z)) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8211,plain,
% 1.85/2.09 (b(s(s(s(elem!1))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8210, 7697, 9, 1355, 1])).
% 1.85/2.09 tff(8212,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(z, 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(X0, 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, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8213,plain,
% 1.85/2.09 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8214,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, 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, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[8213])).
% 1.85/2.09 tff(8215,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, 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, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[8214, 8212])).
% 1.85/2.09 tff(8216,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(8217,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[8216, 8215])).
% 1.85/2.09 tff(8218,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8217, 245, 4105, 4186, 1287, 308, 1427])).
% 1.85/2.09 tff(8219,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8220,plain,
% 1.85/2.09 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8219, 4105, 4186, 308, 1427])).
% 1.85/2.09 tff(8221,plain,
% 1.85/2.09 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[353, 8220, 11])).
% 1.85/2.09 tff(8222,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2416, 141, 371, 1342, 2069])).
% 1.85/2.09 tff(8223,plain,((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8224,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8223, 4907, 7716, 8221])).
% 1.85/2.09 tff(8225,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(8226,plain,
% 1.85/2.09 (~b(z, elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[8225, 11, 1427, 308, 4186])).
% 1.85/2.09 tff(8227,plain,
% 1.85/2.09 (r(z, elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[175, 8226, 55])).
% 1.85/2.09 tff(8228,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.85/2.09 tff(8229,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8230,plain,
% 1.85/2.09 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(8231,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8230])).
% 1.85/2.10 tff(8232,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[8231, 8229])).
% 1.85/2.10 tff(8233,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(8234,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[8233, 8232])).
% 1.85/2.10 tff(8235,plain,
% 1.85/2.10 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8234, 245, 308, 1427, 6550])).
% 1.85/2.10 tff(8236,plain,
% 1.85/2.10 (r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2091, 32, 8235, 8228])).
% 1.85/2.10 tff(8237,plain,
% 1.85/2.10 (~r(z, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8223, 2069, 371])).
% 1.85/2.10 tff(8238,plain,
% 1.85/2.10 (b(z, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[644, 8237])).
% 1.85/2.10 tff(8239,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8240,plain,
% 1.85/2.10 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8241,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8240])).
% 1.85/2.10 tff(8242,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[8241, 8239])).
% 1.85/2.10 tff(8243,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(8244,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[8243, 8242])).
% 1.85/2.10 tff(8245,plain,
% 1.85/2.10 (~b(s(elem!1), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8244, 245, 4186, 308, 8238])).
% 1.85/2.10 tff(8246,plain,
% 1.85/2.10 (r(s(elem!1), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1039, 8245])).
% 1.85/2.10 tff(8247,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[4414, 141, 8246, 1355, 8236])).
% 1.85/2.10 tff(8248,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (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, z)) | (elem!1 = s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(8249,plain,
% 1.85/2.10 (~r(z, s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8248, 371, 8228, 308, 1427, 4186, 1717, 289, 1355])).
% 1.85/2.10 tff(8250,plain,
% 1.85/2.10 (b(z, s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[197, 8249])).
% 1.85/2.10 tff(8251,plain,
% 1.85/2.10 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8252,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8251])).
% 1.85/2.10 tff(8253,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[8252, 3363])).
% 1.85/2.10 tff(8254,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(8255,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[8254, 8253])).
% 1.85/2.10 tff(8256,plain,
% 1.85/2.10 (~b(elem!1, s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8255, 245, 4186, 1427, 8250])).
% 1.85/2.10 tff(8257,plain,
% 1.85/2.10 (r(elem!1, s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1724, 8256, 1717])).
% 1.85/2.10 tff(8258,plain,
% 1.85/2.10 (~r(elem!1, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2762, 8257, 371])).
% 1.85/2.10 tff(8259,plain,
% 1.85/2.10 (b(elem!1, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2777, 8258, 2774])).
% 1.85/2.10 tff(8260,plain,
% 1.85/2.10 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2334, 8259, 308, 1427])).
% 1.85/2.10 tff(8261,plain,
% 1.85/2.10 (r(s(elem!1), s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2091, 32, 8260, 8228])).
% 1.85/2.10 tff(8262,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8263,plain,
% 1.85/2.10 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8264,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8263])).
% 1.85/2.10 tff(8265,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)))),
% 1.85/2.10 inference(transitivity,[status(thm)],[8264, 8262])).
% 1.85/2.10 tff(8266,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(8267,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(elem!1), z))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[8266, 8265])).
% 1.85/2.10 tff(8268,plain,
% 1.85/2.10 (~b(s(elem!1), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8267, 245, 4186, 308, 1427, 8250])).
% 1.85/2.10 tff(8269,plain,
% 1.85/2.10 (r(s(elem!1), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1039, 8268])).
% 1.85/2.10 tff(8270,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[4414, 141, 8269, 1355, 8261])).
% 1.85/2.10 tff(8271,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(8272,plain,
% 1.85/2.10 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8271, 8125, 1355, 308, 1427, 2774, 1717, 4186, 8227])).
% 1.85/2.10 tff(8273,plain,
% 1.85/2.10 (b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[353, 8272, 11])).
% 1.85/2.10 tff(8274,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(z, 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(X0, 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, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8275,plain,
% 1.85/2.10 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(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, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8276,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(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(X0, 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, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8275])).
% 1.85/2.10 tff(8277,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(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(X0, 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, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[8276, 8274])).
% 1.85/2.10 tff(8278,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(8279,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[8278, 8277])).
% 1.85/2.10 tff(8280,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8279, 245, 4186, 1287, 308, 1427, 838])).
% 1.85/2.10 tff(8281,plain,((~b(z, 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(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(8282,plain,
% 1.85/2.10 (~b(z, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8281, 8273, 4186, 308, 1427])).
% 1.85/2.10 tff(8283,plain,
% 1.85/2.10 (r(z, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[644, 8282])).
% 1.85/2.10 tff(8284,plain,
% 1.85/2.10 (((~![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))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8285,plain,
% 1.85/2.10 (((~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))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8286,plain,
% 1.85/2.10 (((~![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)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8285])).
% 1.85/2.10 tff(8287,plain,
% 1.85/2.10 (((~![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))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[8286, 8284])).
% 1.85/2.10 tff(8288,plain,
% 1.85/2.10 ((~![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)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(8289,plain,
% 1.85/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[8288, 8287])).
% 1.85/2.10 tff(8290,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8289, 141, 289, 1342, 1367])).
% 1.85/2.10 tff(8291,plain,((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(8292,plain,
% 1.85/2.10 (~r(elem!1, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8291, 8227, 8283])).
% 1.85/2.10 tff(8293,plain,
% 1.85/2.10 (b(elem!1, s(elem!1))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2777, 8292, 2774])).
% 1.85/2.10 tff(8294,plain,
% 1.85/2.10 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(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(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(elem!1))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8295,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8294])).
% 1.85/2.10 tff(8296,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[8295, 2018])).
% 1.85/2.10 tff(8297,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(8298,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[8297, 8296])).
% 1.85/2.10 tff(8299,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8298, 245, 8273, 308, 1427, 8293])).
% 1.85/2.10 tff(8300,plain,((s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (elem!1 = s(s(s(elem!1)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(8301,plain,
% 1.85/2.10 (s(s(s(elem!1))) = s(elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[8300, 8211, 7316, 2563, 7697, 1355, 1673, 118])).
% 1.85/2.10 tff(8302,plain,
% 1.85/2.10 (elem!1 = s(s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1957, 8301])).
% 1.85/2.10 tff(8303,plain,
% 1.85/2.10 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8302])).
% 1.85/2.10 tff(8304,plain,
% 1.85/2.10 (s(s(s(s(elem!1)))) = elem!1),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2567, 8302])).
% 1.85/2.10 tff(8305,plain,
% 1.85/2.10 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1051, 8304])).
% 1.85/2.10 tff(8306,plain,
% 1.85/2.10 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[775, 8305])).
% 1.85/2.10 tff(8307,plain,
% 1.85/2.10 (s(s(s(s(elem!1)))) = elem!1),
% 1.85/2.10 inference(symmetry,[status(thm)],[8302])).
% 1.85/2.10 tff(8308,plain,
% 1.85/2.10 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8307])).
% 1.85/2.10 tff(8309,plain,
% 1.85/2.10 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.85/2.10 inference(transitivity,[status(thm)],[8308, 339])).
% 1.85/2.10 tff(8310,plain,
% 1.85/2.10 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8309])).
% 1.85/2.10 tff(8311,plain,
% 1.85/2.10 (~(s(z) = elem!1)),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[209, 8310])).
% 1.85/2.10 tff(8312,plain,
% 1.85/2.10 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1065, 8304, 9])).
% 1.85/2.10 tff(8313,plain,
% 1.85/2.10 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[553])).
% 1.85/2.10 tff(8314,plain,
% 1.85/2.10 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 1.85/2.10 inference(symmetry,[status(thm)],[8313])).
% 1.85/2.10 tff(8315,plain,
% 1.85/2.10 (elem!1 = s(s(s(s(elem!1))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1957, 553])).
% 1.85/2.10 tff(8316,plain,
% 1.85/2.10 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8315])).
% 1.85/2.10 tff(8317,plain,
% 1.85/2.10 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[4186, 8316])).
% 1.85/2.10 tff(8318,plain,
% 1.85/2.10 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8315])).
% 1.85/2.10 tff(8319,plain,
% 1.85/2.10 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[308, 8318])).
% 1.85/2.10 tff(8320,plain,
% 1.85/2.10 (b(z, s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[4808, 4105, 8315])).
% 1.85/2.10 tff(8321,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8322,plain,
% 1.85/2.10 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(8323,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[8322])).
% 1.85/2.10 tff(8324,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8323, 8321])).
% 1.85/2.11 tff(8325,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(8326,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8325, 8324])).
% 1.85/2.11 tff(8327,plain,
% 1.85/2.11 (~b(z, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8326, 245, 8320, 8319, 8317])).
% 1.85/2.11 tff(8328,plain,
% 1.85/2.11 (r(z, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[644, 8327])).
% 1.85/2.11 tff(8329,plain,
% 1.85/2.11 (r(z, s(s(s(elem!1))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8328, 8314])).
% 1.85/2.11 tff(8330,plain,
% 1.85/2.11 (s(s(s(s(elem!1)))) = elem!1),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2567, 8315])).
% 1.85/2.11 tff(8331,plain,
% 1.85/2.11 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6872, 8330])).
% 1.85/2.11 tff(8332,plain,
% 1.85/2.11 (s(s(s(s(elem!1)))) = elem!1),
% 1.85/2.11 inference(symmetry,[status(thm)],[8315])).
% 1.85/2.11 tff(8333,plain,
% 1.85/2.11 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8332])).
% 1.85/2.11 tff(8334,plain,
% 1.85/2.11 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8333])).
% 1.85/2.11 tff(8335,plain,
% 1.85/2.11 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8334, 255, 848, 49, 8315])).
% 1.85/2.11 tff(8336,plain,
% 1.85/2.11 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8335])).
% 1.85/2.11 tff(8337,plain,
% 1.85/2.11 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 1.85/2.11 inference(transitivity,[status(thm)],[8336, 8333])).
% 1.85/2.11 tff(8338,plain,
% 1.85/2.11 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8337])).
% 1.85/2.11 tff(8339,plain,
% 1.85/2.11 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.11 inference(symmetry,[status(thm)],[8338])).
% 1.85/2.11 tff(8340,plain,
% 1.85/2.11 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8339])).
% 1.85/2.11 tff(8341,plain,
% 1.85/2.11 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), elem!1)),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8332])).
% 1.85/2.11 tff(8342,plain,
% 1.85/2.11 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(symmetry,[status(thm)],[8341])).
% 1.85/2.11 tff(8343,plain,
% 1.85/2.11 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8332])).
% 1.85/2.11 tff(8344,plain,
% 1.85/2.11 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.85/2.11 inference(transitivity,[status(thm)],[8343, 339])).
% 1.85/2.11 tff(8345,plain,
% 1.85/2.11 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8344])).
% 1.85/2.11 tff(8346,plain,
% 1.85/2.11 (~(s(z) = elem!1)),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[209, 8345])).
% 1.85/2.11 tff(8347,plain,
% 1.85/2.11 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1051, 8330])).
% 1.85/2.11 tff(8348,plain,
% 1.85/2.11 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[775, 8347])).
% 1.85/2.11 tff(8349,plain,
% 1.85/2.11 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6941, 4105, 1427, 4186, 8330])).
% 1.85/2.11 tff(8350,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[787, 8349, 8348])).
% 1.85/2.11 tff(8351,plain,
% 1.85/2.11 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8315])).
% 1.85/2.11 tff(8352,plain,
% 1.85/2.11 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), elem!1)),
% 1.85/2.11 inference(symmetry,[status(thm)],[8351])).
% 1.85/2.11 tff(8353,plain,
% 1.85/2.11 ((~b(s(z), s(s(s(s(elem!1)))))) <=> (~b(s(z), elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8352])).
% 1.85/2.11 tff(8354,plain,
% 1.85/2.11 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[553])).
% 1.85/2.11 tff(8355,plain,
% 1.85/2.11 (b(s(elem!1), s(z))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[2179, 8354])).
% 1.85/2.11 tff(8356,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8357,plain,
% 1.85/2.11 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8358,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8357])).
% 1.85/2.11 tff(8359,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8358, 8356])).
% 1.85/2.11 tff(8360,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(8361,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8360, 8359])).
% 1.85/2.11 tff(8362,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8361, 245, 4188, 2197, 556, 1943, 3380])).
% 1.85/2.11 tff(8363,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(8364,plain,
% 1.85/2.11 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8363, 8355, 2197, 8319, 1943])).
% 1.85/2.11 tff(8365,plain,
% 1.85/2.11 (~b(s(z), elem!1)),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8364, 8353])).
% 1.85/2.11 tff(8366,plain,
% 1.85/2.11 (r(s(z), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[389, 8365, 8346])).
% 1.85/2.11 tff(8367,plain,
% 1.85/2.11 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8366, 8342])).
% 1.85/2.11 tff(8368,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8315])).
% 1.85/2.11 tff(8369,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[2628, 8368])).
% 1.85/2.11 tff(8370,plain,
% 1.85/2.11 (((~![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(z))))), s(z))) | (~r(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8371,plain,
% 1.85/2.11 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8372,plain,
% 1.85/2.11 (((~![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(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8371])).
% 1.85/2.11 tff(8373,plain,
% 1.85/2.11 (((~![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(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8372, 8370])).
% 1.85/2.11 tff(8374,plain,
% 1.85/2.11 ((~![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(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(8375,plain,
% 1.85/2.11 ((~![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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8374, 8373])).
% 1.85/2.11 tff(8376,plain,
% 1.85/2.11 (~r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8375, 141, 8369, 8367])).
% 1.85/2.11 tff(8377,plain,
% 1.85/2.11 (b(s(s(s(s(s(z))))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[809, 8376])).
% 1.85/2.11 tff(8378,plain,
% 1.85/2.11 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[553])).
% 1.85/2.11 tff(8379,plain,
% 1.85/2.11 (b(s(z), s(elem!1))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[2111, 8378])).
% 1.85/2.11 tff(8380,plain,
% 1.85/2.11 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6904, 245, 8379, 8355, 8377])).
% 1.85/2.11 tff(8381,plain,
% 1.85/2.11 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1156, 32, 1153, 8380])).
% 1.85/2.11 tff(8382,plain,
% 1.85/2.11 (~(s(elem!1) = s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[7266, 8330])).
% 1.85/2.11 tff(8383,plain,
% 1.85/2.11 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[553])).
% 1.85/2.11 tff(8384,plain,
% 1.85/2.11 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 1.85/2.11 inference(symmetry,[status(thm)],[8383])).
% 1.85/2.11 tff(8385,plain,
% 1.85/2.11 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8315])).
% 1.85/2.11 tff(8386,plain,
% 1.85/2.11 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.85/2.11 inference(symmetry,[status(thm)],[8385])).
% 1.85/2.11 tff(8387,plain,
% 1.85/2.11 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8386, 8384])).
% 1.85/2.11 tff(8388,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8332])).
% 1.85/2.11 tff(8389,plain,
% 1.85/2.11 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(symmetry,[status(thm)],[8388])).
% 1.85/2.11 tff(8390,plain,
% 1.85/2.11 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8332])).
% 1.85/2.11 tff(8391,plain,
% 1.85/2.11 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8390])).
% 1.85/2.11 tff(8392,plain,
% 1.85/2.11 (~b(z, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8326, 245, 2197, 8319, 1943])).
% 1.85/2.11 tff(8393,plain,
% 1.85/2.11 (r(z, s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[644, 8392])).
% 1.85/2.11 tff(8394,plain,
% 1.85/2.11 (r(z, s(s(s(elem!1))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8393, 8314])).
% 1.85/2.11 tff(8395,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8396,plain,
% 1.85/2.11 (((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8397,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8396])).
% 1.85/2.11 tff(8398,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8397, 8395])).
% 1.85/2.11 tff(8399,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(8400,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8399, 8398])).
% 1.85/2.11 tff(8401,plain,
% 1.85/2.11 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8400, 245, 8379, 8355, 8377])).
% 1.85/2.11 tff(8402,plain,
% 1.85/2.11 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8401, 8340])).
% 1.85/2.11 tff(8403,plain,
% 1.85/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[797, 8402, 8331])).
% 1.85/2.11 tff(8404,plain,
% 1.85/2.11 (~r(s(s(s(s(s(z))))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6965, 8403, 8330, 8394])).
% 1.85/2.11 tff(8405,plain,
% 1.85/2.11 (b(s(s(s(s(s(z))))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[738, 8404])).
% 1.85/2.11 tff(8406,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8407,plain,
% 1.85/2.11 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8408,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8407])).
% 1.85/2.11 tff(8409,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8408, 8406])).
% 1.85/2.11 tff(8410,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(8411,plain,
% 1.85/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8410, 8409])).
% 1.85/2.11 tff(8412,plain,
% 1.85/2.11 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8411, 245, 2197, 1943, 8405])).
% 1.85/2.11 tff(8413,plain,
% 1.85/2.11 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8412, 8391])).
% 1.85/2.11 tff(8414,plain,
% 1.85/2.11 (r(elem!1, s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[720, 8413, 8347])).
% 1.85/2.11 tff(8415,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8414, 8389])).
% 1.85/2.11 tff(8416,plain,
% 1.85/2.11 (((~![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(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), 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(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8417,plain,
% 1.85/2.11 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8418,plain,
% 1.85/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(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(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8417])).
% 1.85/2.11 tff(8419,plain,
% 1.85/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(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(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8418, 8416])).
% 1.85/2.11 tff(8420,plain,
% 1.85/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(8421,plain,
% 1.85/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8420, 8419])).
% 1.85/2.11 tff(8422,plain,
% 1.85/2.11 ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8421, 141, 8381])).
% 1.85/2.11 tff(8423,plain,
% 1.85/2.11 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8422, 8415])).
% 1.85/2.11 tff(8424,plain,
% 1.85/2.11 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[420, 8423, 164])).
% 1.85/2.11 tff(8425,plain,
% 1.85/2.11 (b(elem!1, s(s(s(elem!1))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8424, 8387])).
% 1.85/2.11 tff(8426,plain,
% 1.85/2.11 (~(s(s(s(z))) = elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[5452, 8330])).
% 1.85/2.11 tff(8427,plain,
% 1.85/2.11 (~r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2649, 8366, 2628])).
% 1.85/2.11 tff(8428,plain,
% 1.85/2.11 (b(s(z), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1698, 8427])).
% 1.85/2.11 tff(8429,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6317, 141, 619, 980, 816])).
% 1.85/2.11 tff(8430,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(8431,plain,
% 1.85/2.11 (~r(s(s(s(z))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8430, 816, 619])).
% 1.85/2.11 tff(8432,plain,
% 1.85/2.11 (b(s(s(s(z))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[895, 32, 8431, 892])).
% 1.85/2.11 tff(8433,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.11 tff(8434,plain,
% 1.85/2.11 (~r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8375, 141, 8433, 6411])).
% 1.85/2.11 tff(8435,plain,
% 1.85/2.11 (b(s(s(s(s(s(z))))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[809, 8434])).
% 1.85/2.11 tff(8436,plain,
% 1.85/2.11 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[422])).
% 1.85/2.11 tff(8437,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.85/2.11 inference(symmetry,[status(thm)],[8436])).
% 1.85/2.11 tff(8438,plain,
% 1.85/2.11 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), elem!1))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8437])).
% 1.85/2.11 tff(8439,assumption,(~r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.11 tff(8440,plain,
% 1.85/2.11 (~r(s(s(s(z))), elem!1)),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8439, 8438])).
% 1.85/2.11 tff(8441,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[816, 8440])).
% 1.85/2.11 tff(8442,plain,(r(s(s(s(z))), s(s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)) | (~(elem!1 = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(8443,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8442, 816, 422])).
% 1.85/2.11 tff(8444,plain,
% 1.85/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8445,plain,
% 1.85/2.11 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(8446,plain,
% 1.85/2.11 (((~![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(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[8445])).
% 1.85/2.11 tff(8447,plain,
% 1.85/2.11 (((~![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(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[8446, 8444])).
% 1.85/2.11 tff(8448,plain,
% 1.85/2.11 ((~![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(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(8449,plain,
% 1.85/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[8448, 8447])).
% 1.85/2.11 tff(8450,plain,
% 1.85/2.11 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8449, 141, 8443, 8433])).
% 1.85/2.11 tff(8451,plain,
% 1.85/2.11 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[1515, 8450])).
% 1.85/2.11 tff(8452,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6239, 245, 6306, 8451, 8435, 8432])).
% 1.85/2.11 tff(8453,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(8454,plain,
% 1.85/2.11 (~r(s(s(s(z))), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[8453, 8428, 8369, 8315, 8366])).
% 1.85/2.11 tff(8455,plain,
% 1.85/2.11 (b(s(s(s(z))), elem!1)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[7257, 8454, 8426])).
% 1.85/2.11 tff(8456,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.85/2.11 tff(8457,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8458,plain,
% 1.85/2.12 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8459,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, 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(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8458])).
% 1.85/2.12 tff(8460,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(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(X0, 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(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[8459, 8457])).
% 1.85/2.12 tff(8461,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(8462,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8461, 8460])).
% 1.85/2.12 tff(8463,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8462, 245, 308, 1427, 2101, 954, 8456])).
% 1.85/2.12 tff(8464,plain,((~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(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8465,plain,
% 1.85/2.12 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8464, 8455, 1427, 8425, 308])).
% 1.85/2.12 tff(8466,assumption,(~b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.85/2.12 tff(8467,assumption,(~r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.85/2.12 tff(8468,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[826, 32, 610, 8467, 8466])).
% 1.85/2.12 tff(8469,plain,(r(s(elem!1), s(s(s(z)))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8470,plain,
% 1.85/2.12 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8469, 8465, 8382])).
% 1.85/2.12 tff(8471,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6019, 141, 6013, 930, 6012])).
% 1.85/2.12 tff(8472,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8473,plain,
% 1.85/2.12 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8472, 8470, 8381])).
% 1.85/2.12 tff(8474,plain,
% 1.85/2.12 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1515, 8473])).
% 1.85/2.12 tff(8475,plain,
% 1.85/2.12 (~b(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6239, 245, 8428, 8474, 8377])).
% 1.85/2.12 tff(8476,plain,
% 1.85/2.12 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5923, 1153])).
% 1.85/2.12 tff(8477,plain,
% 1.85/2.12 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5933, 32, 8476, 8401])).
% 1.85/2.12 tff(8478,plain,
% 1.85/2.12 (~r(z, s(s(s(s(s(z))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5984, 141, 8393, 8477])).
% 1.85/2.12 tff(8479,plain,
% 1.85/2.12 (b(z, s(s(s(s(s(z))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[758, 8478])).
% 1.85/2.12 tff(8480,plain,
% 1.85/2.12 (~b(s(s(s(z))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[6247, 245, 8428, 8474, 8479, 8377])).
% 1.85/2.12 tff(8481,plain,
% 1.85/2.12 (r(s(s(s(z))), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7060, 8480])).
% 1.85/2.12 tff(8482,plain,
% 1.85/2.12 (~r(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[985, 8481, 220])).
% 1.85/2.12 tff(8483,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[895, 32, 8482, 892, 8475])).
% 1.85/2.12 tff(8484,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8485,plain,
% 1.85/2.12 (~r(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8484, 8320, 308, 553, 164, 1427, 8317, 1153, 8350, 1355])).
% 1.85/2.12 tff(8486,plain,
% 1.85/2.12 (b(s(z), z)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[232, 8485])).
% 1.85/2.12 tff(8487,plain,
% 1.85/2.12 (~b(s(z), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[4436, 8486, 4105, 4186])).
% 1.85/2.12 tff(8488,plain,
% 1.85/2.12 (r(s(z), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[389, 8487, 8346])).
% 1.85/2.12 tff(8489,plain,
% 1.85/2.12 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8488, 8342])).
% 1.85/2.12 tff(8490,plain,
% 1.85/2.12 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8350, 8368])).
% 1.85/2.12 tff(8491,plain,
% 1.85/2.12 ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8375, 141, 8490])).
% 1.85/2.12 tff(8492,plain,
% 1.85/2.12 (~r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8491, 8489])).
% 1.85/2.12 tff(8493,plain,
% 1.85/2.12 (b(s(s(s(s(s(z))))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[809, 8492])).
% 1.85/2.12 tff(8494,plain,
% 1.85/2.12 (~r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2649, 8488, 8350])).
% 1.85/2.12 tff(8495,plain,
% 1.85/2.12 (b(s(z), s(s(s(s(s(z))))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1698, 8494])).
% 1.85/2.12 tff(8496,plain,
% 1.85/2.12 (~r(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8453, 8495, 8490, 8315, 8488])).
% 1.85/2.12 tff(8497,plain,
% 1.85/2.12 (b(s(s(s(z))), elem!1)),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[7257, 8496, 8426])).
% 1.85/2.12 tff(8498,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8499,plain,
% 1.85/2.12 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8500,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8499])).
% 1.85/2.12 tff(8501,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[8500, 8498])).
% 1.85/2.12 tff(8502,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(8503,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8502, 8501])).
% 1.85/2.12 tff(8504,plain,
% 1.85/2.12 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8503, 245, 8486, 8320, 8317])).
% 1.85/2.12 tff(8505,plain,
% 1.85/2.12 (r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[217, 8504])).
% 1.85/2.12 tff(8506,plain,
% 1.85/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8507,plain,
% 1.85/2.12 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8508,plain,
% 1.85/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(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), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8507])).
% 1.85/2.12 tff(8509,plain,
% 1.85/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(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), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[8508, 8506])).
% 1.85/2.12 tff(8510,plain,
% 1.85/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(8511,plain,
% 1.85/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8510, 8509])).
% 1.85/2.12 tff(8512,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8511, 141, 998, 406, 219])).
% 1.85/2.12 tff(8513,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8514,plain,
% 1.85/2.12 (~r(s(elem!1), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8513, 406, 219])).
% 1.85/2.12 tff(8515,plain,
% 1.85/2.12 (b(s(elem!1), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[369, 8514, 358])).
% 1.85/2.12 tff(8516,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8517,plain,
% 1.85/2.12 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8518,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8517])).
% 1.85/2.12 tff(8519,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[8518, 8516])).
% 1.85/2.12 tff(8520,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(8521,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8520, 8519])).
% 1.85/2.12 tff(8522,plain,
% 1.85/2.12 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8521, 245, 8515, 6306, 709])).
% 1.85/2.12 tff(8523,plain,
% 1.85/2.12 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[5933, 32, 5926, 8522])).
% 1.85/2.12 tff(8524,plain,
% 1.85/2.12 (((~![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(z))))), s(elem!1))) | (~r(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)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8525,plain,
% 1.85/2.12 ((~![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(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(8526,plain,
% 1.85/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8525, 8524])).
% 1.85/2.12 tff(8527,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8526, 141, 406, 8433, 8523])).
% 1.85/2.12 tff(8528,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8529,plain,
% 1.85/2.12 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8528, 8490, 8476, 8495, 8493, 358, 8505])).
% 1.85/2.12 tff(8530,plain,
% 1.85/2.12 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[553])).
% 1.85/2.12 tff(8531,plain,
% 1.85/2.12 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 1.85/2.12 inference(symmetry,[status(thm)],[8530])).
% 1.85/2.12 tff(8532,plain,
% 1.85/2.12 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8315])).
% 1.85/2.12 tff(8533,plain,
% 1.85/2.12 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.85/2.12 inference(symmetry,[status(thm)],[8532])).
% 1.85/2.12 tff(8534,plain,
% 1.85/2.12 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[8533, 8531])).
% 1.85/2.12 tff(8535,plain,
% 1.85/2.12 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8534])).
% 1.85/2.12 tff(8536,assumption,(~r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.85/2.12 tff(8537,plain,
% 1.85/2.12 (~r(elem!1, s(s(s(elem!1))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8536, 8535])).
% 1.85/2.12 tff(8538,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[2070, 8537])).
% 1.85/2.12 tff(8539,plain,(r(s(s(s(s(elem!1)))), s(elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8540,plain,
% 1.85/2.12 (~r(elem!1, s(s(s(elem!1))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8539, 8529, 553])).
% 1.85/2.12 tff(8541,plain,
% 1.85/2.12 (b(elem!1, s(s(s(elem!1))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1724, 8540, 1717])).
% 1.85/2.12 tff(8542,plain,
% 1.85/2.12 (~b(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8464, 8541, 1427, 8497, 308])).
% 1.85/2.12 tff(8543,plain,
% 1.85/2.12 (r(s(elem!1), s(s(s(z))))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8469, 8542, 8382])).
% 1.85/2.12 tff(8544,plain,
% 1.85/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8545,plain,
% 1.85/2.12 (((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8546,plain,
% 1.85/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8545])).
% 1.85/2.12 tff(8547,plain,
% 1.85/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[8546, 8544])).
% 1.85/2.12 tff(8548,plain,
% 1.85/2.12 ((~![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))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(8549,plain,
% 1.85/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.85/2.12 inference(modus_ponens,[status(thm)],[8548, 8547])).
% 1.85/2.12 tff(8550,plain,
% 1.85/2.12 ($false),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8549, 141, 998, 980, 930])).
% 1.85/2.12 tff(8551,plain,((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.12 tff(8552,plain,
% 1.85/2.12 (~r(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[8551, 998, 930])).
% 1.85/2.12 tff(8553,plain,
% 1.85/2.12 (b(s(s(s(z))), s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[895, 32, 8552, 892])).
% 1.85/2.12 tff(8554,plain,
% 1.85/2.12 (~r(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[4743, 998, 1342])).
% 1.85/2.12 tff(8555,plain,
% 1.85/2.12 (b(z, s(z))),
% 1.85/2.12 inference(unit_resolution,[status(thm)],[1421, 8554])).
% 1.85/2.12 tff(8556,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~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))))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8557,plain,
% 1.85/2.12 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~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))))))))),
% 1.85/2.12 inference(rewrite,[status(thm)],[])).
% 1.85/2.12 tff(8558,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~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)))))))))),
% 1.85/2.12 inference(monotonicity,[status(thm)],[8557])).
% 1.85/2.12 tff(8559,plain,
% 1.85/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~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))))))))),
% 1.85/2.12 inference(transitivity,[status(thm)],[8558, 8556])).
% 1.85/2.12 tff(8560,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~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))))))))),
% 1.85/2.12 inference(quant_inst,[status(thm)],[])).
% 1.85/2.12 tff(8561,plain,
% 1.85/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~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)))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 1.96/2.13 tff(8562,plain,
% 1.96/2.13 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8561, 245, 355, 2197, 709])).
% 1.96/2.13 tff(8563,plain,
% 1.96/2.13 (~b(z, s(s(s(s(s(z))))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8562, 8555])).
% 1.96/2.13 tff(8564,plain,
% 1.96/2.13 (r(z, s(s(s(s(s(z))))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[758, 8563])).
% 1.96/2.13 tff(8565,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.96/2.13 tff(8566,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8567,plain,
% 1.96/2.13 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8568,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8567])).
% 1.96/2.13 tff(8569,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8568, 8566])).
% 1.96/2.13 tff(8570,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8571,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8570, 8569])).
% 1.96/2.13 tff(8572,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8571, 245, 355, 4187, 911, 8565])).
% 1.96/2.13 tff(8573,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8574,plain,
% 1.96/2.13 (~b(s(s(s(z))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8573, 8553, 8555, 355])).
% 1.96/2.13 tff(8575,plain,
% 1.96/2.13 (r(s(s(s(z))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[7060, 8574])).
% 1.96/2.13 tff(8576,plain,
% 1.96/2.13 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[7090, 8575, 8564])).
% 1.96/2.13 tff(8577,plain,
% 1.96/2.13 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1515, 8576])).
% 1.96/2.13 tff(8578,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8579,plain,
% 1.96/2.13 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8580,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8579])).
% 1.96/2.13 tff(8581,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8580, 8578])).
% 1.96/2.13 tff(8582,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8583,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8582, 8581])).
% 1.96/2.13 tff(8584,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8583, 245, 355, 8555, 8577, 709, 8553])).
% 1.96/2.13 tff(8585,plain,((~r(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8586,plain,
% 1.96/2.13 (~r(s(elem!1), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8585, 8486, 8493, 8543, 8320, 8328])).
% 1.96/2.13 tff(8587,plain,
% 1.96/2.13 (b(s(elem!1), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[369, 8586, 358])).
% 1.96/2.13 tff(8588,plain,
% 1.96/2.13 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8521, 245, 8587, 8495, 8493])).
% 1.96/2.13 tff(8589,plain,
% 1.96/2.13 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8588, 8340])).
% 1.96/2.13 tff(8590,plain,
% 1.96/2.13 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[797, 8589, 8331])).
% 1.96/2.13 tff(8591,plain,
% 1.96/2.13 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6965, 8590, 8330, 8329])).
% 1.96/2.13 tff(8592,plain,
% 1.96/2.13 (b(s(s(s(s(s(z))))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[738, 8591])).
% 1.96/2.13 tff(8593,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8594,plain,
% 1.96/2.13 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8595,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8594])).
% 1.96/2.13 tff(8596,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8595, 8593])).
% 1.96/2.13 tff(8597,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8598,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8597, 8596])).
% 1.96/2.13 tff(8599,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8598, 245, 8486, 8320, 8317, 8495, 8592])).
% 1.96/2.13 tff(8600,plain,((~b(z, elem!1)) | (~(s(s(s(elem!1))) = s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, z)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8601,plain,
% 1.96/2.13 (~b(z, elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8600, 8301, 348, 8211, 7316, 1673, 7697, 7, 8312, 1355])).
% 1.96/2.13 tff(8602,plain,
% 1.96/2.13 (r(z, elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[175, 8601, 118])).
% 1.96/2.13 tff(8603,plain,
% 1.96/2.13 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8301])).
% 1.96/2.13 tff(8604,plain,
% 1.96/2.13 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(symmetry,[status(thm)],[8603])).
% 1.96/2.13 tff(8605,plain,
% 1.96/2.13 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8302])).
% 1.96/2.13 tff(8606,plain,
% 1.96/2.13 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[7697, 8605])).
% 1.96/2.13 tff(8607,plain,
% 1.96/2.13 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8302])).
% 1.96/2.13 tff(8608,plain,
% 1.96/2.13 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[7316, 8607])).
% 1.96/2.13 tff(8609,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.96/2.13 tff(8610,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[668, 141, 289, 220, 619])).
% 1.96/2.13 tff(8611,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8612,plain,
% 1.96/2.13 (~r(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8611, 289, 220])).
% 1.96/2.13 tff(8613,plain,
% 1.96/2.13 (b(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[389, 8612, 8609])).
% 1.96/2.13 tff(8614,plain,
% 1.96/2.13 (~r(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6573, 8613, 4186, 1427, 1717, 289])).
% 1.96/2.13 tff(8615,plain,
% 1.96/2.13 (b(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[197, 8614])).
% 1.96/2.13 tff(8616,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6593, 245, 4186, 1427, 8615, 8613, 3615])).
% 1.96/2.13 tff(8617,plain,((~r(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (s(z) = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8618,plain,
% 1.96/2.13 (~b(s(z), s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8617, 220, 1427, 4186, 1717, 289, 8609])).
% 1.96/2.13 tff(8619,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1133, 8618, 2110])).
% 1.96/2.13 tff(8620,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(z) = elem!1) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8621,plain,
% 1.96/2.13 (~r(s(z), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8620, 8211, 7697, 1673, 8602, 8311, 1355])).
% 1.96/2.13 tff(8622,plain,
% 1.96/2.13 (b(s(z), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[232, 8621])).
% 1.96/2.13 tff(8623,plain,
% 1.96/2.13 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[422])).
% 1.96/2.13 tff(8624,plain,
% 1.96/2.13 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6408])).
% 1.96/2.13 tff(8625,plain,
% 1.96/2.13 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.96/2.13 inference(transitivity,[status(thm)],[8624, 339])).
% 1.96/2.13 tff(8626,plain,
% 1.96/2.13 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8625])).
% 1.96/2.13 tff(8627,plain,
% 1.96/2.13 (~(s(z) = elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[209, 8626])).
% 1.96/2.13 tff(8628,plain,
% 1.96/2.13 ((~r(s(z), s(s(s(s(elem!1)))))) <=> (~r(s(z), elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6409])).
% 1.96/2.13 tff(8629,plain,
% 1.96/2.13 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4580, 245, 838, 556, 1943])).
% 1.96/2.13 tff(8630,plain,
% 1.96/2.13 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[420, 8629, 164])).
% 1.96/2.13 tff(8631,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8632,plain,
% 1.96/2.13 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))) <=> ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8633,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8632])).
% 1.96/2.13 tff(8634,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8633, 8631])).
% 1.96/2.13 tff(8635,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8636,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8635, 8634])).
% 1.96/2.13 tff(8637,plain,
% 1.96/2.13 (~b(s(z), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8636, 245, 355, 838, 556, 1943])).
% 1.96/2.13 tff(8638,plain,
% 1.96/2.13 (r(s(z), s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[440, 8637, 9])).
% 1.96/2.13 tff(8639,plain,
% 1.96/2.13 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), 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(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8640,plain,
% 1.96/2.13 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8641,plain,
% 1.96/2.13 (((~![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(z), 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(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8640])).
% 1.96/2.13 tff(8642,plain,
% 1.96/2.13 (((~![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(z), 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(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8641, 8639])).
% 1.96/2.13 tff(8643,plain,
% 1.96/2.13 ((~![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(z), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8644,plain,
% 1.96/2.13 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8643, 8642])).
% 1.96/2.13 tff(8645,plain,
% 1.96/2.13 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8644, 141, 8638, 8630])).
% 1.96/2.13 tff(8646,plain,
% 1.96/2.13 (~r(s(z), elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8645, 8628])).
% 1.96/2.13 tff(8647,plain,
% 1.96/2.13 (b(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[389, 8646, 8627])).
% 1.96/2.13 tff(8648,plain,
% 1.96/2.13 (b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8647, 8623])).
% 1.96/2.13 tff(8649,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8650,plain,
% 1.96/2.13 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8651,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8650])).
% 1.96/2.13 tff(8652,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8651, 8649])).
% 1.96/2.13 tff(8653,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8654,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8653, 8652])).
% 1.96/2.13 tff(8655,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8654, 245, 355, 838, 556, 1943, 8648])).
% 1.96/2.13 tff(8656,plain,((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8657,plain,
% 1.96/2.13 (~b(z, s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8656, 8622, 8608, 8606, 8302, 7, 9])).
% 1.96/2.13 tff(8658,plain,
% 1.96/2.13 (r(z, s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[644, 8657])).
% 1.96/2.13 tff(8659,plain,
% 1.96/2.13 (r(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8658, 8604])).
% 1.96/2.13 tff(8660,plain,
% 1.96/2.13 (~b(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6573, 8659, 7697, 8211, 1673, 8602])).
% 1.96/2.13 tff(8661,plain,
% 1.96/2.14 (r(s(z), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[389, 8660, 8311])).
% 1.96/2.14 tff(8662,plain,
% 1.96/2.14 (r(z, elem!1) <=> r(z, s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8302])).
% 1.96/2.14 tff(8663,plain,
% 1.96/2.14 (r(z, s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8602, 8662])).
% 1.96/2.14 tff(8664,plain,
% 1.96/2.14 (~r(z, s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6420, 8661, 8302, 8663])).
% 1.96/2.14 tff(8665,plain,
% 1.96/2.14 (b(z, s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1421, 8664])).
% 1.96/2.14 tff(8666,plain,
% 1.96/2.14 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6424, 8665, 8602, 8622, 8661])).
% 1.96/2.14 tff(8667,plain,
% 1.96/2.14 (b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[787, 8666, 8306])).
% 1.96/2.14 tff(8668,plain,
% 1.96/2.14 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8667, 8303])).
% 1.96/2.14 tff(8669,plain,
% 1.96/2.14 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6872, 8304])).
% 1.96/2.14 tff(8670,plain,
% 1.96/2.14 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8307])).
% 1.96/2.14 tff(8671,plain,
% 1.96/2.14 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8301])).
% 1.96/2.14 tff(8672,plain,
% 1.96/2.14 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8670])).
% 1.96/2.14 tff(8673,plain,
% 1.96/2.14 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8672, 255, 8671, 49, 8302])).
% 1.96/2.14 tff(8674,plain,
% 1.96/2.14 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8673])).
% 1.96/2.14 tff(8675,plain,
% 1.96/2.14 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 1.96/2.14 inference(transitivity,[status(thm)],[8674, 8670])).
% 1.96/2.14 tff(8676,plain,
% 1.96/2.14 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8675])).
% 1.96/2.14 tff(8677,plain,
% 1.96/2.14 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8676])).
% 1.96/2.14 tff(8678,plain,
% 1.96/2.14 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8677])).
% 1.96/2.14 tff(8679,plain,
% 1.96/2.14 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3674, 8658, 8663])).
% 1.96/2.14 tff(8680,plain,
% 1.96/2.14 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[420, 8679, 7])).
% 1.96/2.14 tff(8681,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8682,plain,
% 1.96/2.14 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), 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(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8683,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8682])).
% 1.96/2.14 tff(8684,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8683, 8681])).
% 1.96/2.14 tff(8685,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8686,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8685, 8684])).
% 1.96/2.14 tff(8687,plain,
% 1.96/2.14 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8686, 245, 8608, 8680, 8668])).
% 1.96/2.14 tff(8688,plain,
% 1.96/2.14 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8687, 8678])).
% 1.96/2.14 tff(8689,plain,
% 1.96/2.14 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[797, 8688, 8669])).
% 1.96/2.14 tff(8690,plain,
% 1.96/2.14 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6965, 8689, 8304, 8659])).
% 1.96/2.14 tff(8691,plain,
% 1.96/2.14 (b(s(s(s(s(s(z))))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[738, 8690])).
% 1.96/2.14 tff(8692,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8693,plain,
% 1.96/2.14 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8694,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8693])).
% 1.96/2.14 tff(8695,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8694, 8692])).
% 1.96/2.14 tff(8696,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8697,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8696, 8695])).
% 1.96/2.14 tff(8698,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8697, 245, 8622, 8606, 8665, 8691, 8668])).
% 1.96/2.14 tff(8699,plain,((s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(8700,plain,
% 1.96/2.14 (r(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8699, 7695, 1, 38])).
% 1.96/2.14 tff(8701,plain,
% 1.96/2.14 (~r(elem!1, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4128, 8700, 38])).
% 1.96/2.14 tff(8702,plain,
% 1.96/2.14 (r(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8699, 9, 1, 1355])).
% 1.96/2.14 tff(8703,plain,
% 1.96/2.14 (~r(s(s(s(elem!1))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2041, 141, 8702, 1355])).
% 1.96/2.14 tff(8704,plain,
% 1.96/2.14 (b(s(s(s(elem!1))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[110, 8703, 96])).
% 1.96/2.14 tff(8705,plain,
% 1.96/2.14 (~r(elem!1, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4128, 8702, 1355])).
% 1.96/2.14 tff(8706,plain,
% 1.96/2.14 (b(elem!1, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1724, 8705, 1673])).
% 1.96/2.14 tff(8707,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8708,plain,
% 1.96/2.14 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8709,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8708])).
% 1.96/2.14 tff(8710,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8709, 8707])).
% 1.96/2.14 tff(8711,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8712,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8711, 8710])).
% 1.96/2.14 tff(8713,plain,
% 1.96/2.14 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8712, 245, 7316, 8704, 8706])).
% 1.96/2.14 tff(8714,plain,
% 1.96/2.14 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[428, 426, 10])).
% 1.96/2.14 tff(8715,plain,
% 1.96/2.14 (r(elem!1, s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2777, 426, 2563])).
% 1.96/2.14 tff(8716,plain,
% 1.96/2.14 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[401, 8714])).
% 1.96/2.14 tff(8717,plain,
% 1.96/2.14 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[151, 8716, 8])).
% 1.96/2.14 tff(8718,plain,
% 1.96/2.14 (~r(z, s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4639, 8715, 131])).
% 1.96/2.14 tff(8719,plain,
% 1.96/2.14 (b(z, s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[644, 8718])).
% 1.96/2.14 tff(8720,plain,
% 1.96/2.14 (~r(s(elem!1), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1082, 8715, 131])).
% 1.96/2.14 tff(8721,plain,
% 1.96/2.14 (b(s(elem!1), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1039, 8720])).
% 1.96/2.14 tff(8722,plain,
% 1.96/2.14 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[146, 8717, 131])).
% 1.96/2.14 tff(8723,plain,
% 1.96/2.14 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2558, 8722])).
% 1.96/2.14 tff(8724,plain,
% 1.96/2.14 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3304, 8723, 8721, 8719])).
% 1.96/2.14 tff(8725,plain,
% 1.96/2.14 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1263, 8724, 1])).
% 1.96/2.14 tff(8726,plain,
% 1.96/2.14 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1445, 8725, 105, 1427, 8717, 8715, 8714, 10])).
% 1.96/2.14 tff(8727,plain,
% 1.96/2.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1957, 8714])).
% 1.96/2.14 tff(8728,plain,
% 1.96/2.14 (r(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[353, 8727, 5568])).
% 1.96/2.14 tff(8729,plain,
% 1.96/2.14 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2377, 8725, 8728])).
% 1.96/2.14 tff(8730,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1239, 8729, 8726, 1304])).
% 1.96/2.14 tff(8731,plain,(b(elem!1, s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(elem!1, z)) | b(s(s(s(elem!1))), s(elem!1)) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(8732,plain,
% 1.96/2.14 (b(elem!1, s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8731, 8, 10, 1, 8702, 8713, 8704])).
% 1.96/2.14 tff(8733,plain,
% 1.96/2.14 (r(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[353, 11, 8713])).
% 1.96/2.14 tff(8734,plain,
% 1.96/2.14 (~b(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8300, 11, 7316, 2563, 8704, 1355, 1673, 118])).
% 1.96/2.14 tff(8735,plain,
% 1.96/2.14 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6470, 8, 1, 90, 9, 89])).
% 1.96/2.14 tff(8736,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2558, 8735, 2554])).
% 1.96/2.14 tff(8737,plain,(b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | b(z, elem!1) | (s(z) = s(elem!1)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(8738,plain,
% 1.96/2.14 (b(z, elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8737, 8734, 9, 1, 8])).
% 1.96/2.14 tff(8739,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8740,plain,
% 1.96/2.14 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, 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(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8741,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8740])).
% 1.96/2.14 tff(8742,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8741, 8739])).
% 1.96/2.14 tff(8743,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8744,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8743, 8742])).
% 1.96/2.14 tff(8745,plain,
% 1.96/2.14 (~b(z, s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8744, 245, 8738, 7316, 8704, 8706])).
% 1.96/2.14 tff(8746,plain,
% 1.96/2.14 (r(z, s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[644, 8745])).
% 1.96/2.14 tff(8747,plain,
% 1.96/2.14 (~b(z, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4156, 245, 8738, 8704, 8706])).
% 1.96/2.14 tff(8748,plain,
% 1.96/2.14 (r(z, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[197, 8747])).
% 1.96/2.14 tff(8749,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8223, 8748, 8746, 8733])).
% 1.96/2.14 tff(8750,plain,((s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(8751,plain,
% 1.96/2.14 (s(s(s(elem!1))) = s(elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8750, 8, 1, 9, 1355])).
% 1.96/2.14 tff(8752,plain,
% 1.96/2.14 (elem!1 = s(s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1957, 8751])).
% 1.96/2.14 tff(8753,plain,
% 1.96/2.14 (s(s(s(s(elem!1)))) = elem!1),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2567, 8752])).
% 1.96/2.14 tff(8754,plain,
% 1.96/2.14 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1065, 8753, 9])).
% 1.96/2.14 tff(8755,plain,
% 1.96/2.14 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[5923, 8754])).
% 1.96/2.14 tff(8756,plain,
% 1.96/2.14 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1051, 8753])).
% 1.96/2.14 tff(8757,plain,
% 1.96/2.14 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[775, 8756])).
% 1.96/2.14 tff(8758,plain,
% 1.96/2.14 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8751])).
% 1.96/2.14 tff(8759,plain,
% 1.96/2.14 (r(s(elem!1), z)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[1355, 8758])).
% 1.96/2.14 tff(8760,plain,
% 1.96/2.14 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[5942, 8759, 8702, 8757, 8755, 8732, 7316])).
% 1.96/2.14 tff(8761,plain,
% 1.96/2.14 (b(s(s(s(s(s(z))))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[738, 8760])).
% 1.96/2.14 tff(8762,plain,
% 1.96/2.14 (s(s(s(s(elem!1)))) = elem!1),
% 1.96/2.14 inference(symmetry,[status(thm)],[8752])).
% 1.96/2.14 tff(8763,plain,
% 1.96/2.14 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8762])).
% 1.96/2.14 tff(8764,plain,
% 1.96/2.14 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8763])).
% 1.96/2.14 tff(8765,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8762])).
% 1.96/2.14 tff(8766,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 1.96/2.14 inference(transitivity,[status(thm)],[8765, 339])).
% 1.96/2.14 tff(8767,plain,
% 1.96/2.14 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8766])).
% 1.96/2.14 tff(8768,plain,
% 1.96/2.14 (~(s(z) = elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[209, 8767])).
% 1.96/2.14 tff(8769,plain,
% 1.96/2.14 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8752])).
% 1.96/2.14 tff(8770,plain,
% 1.96/2.14 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), elem!1)),
% 1.96/2.14 inference(symmetry,[status(thm)],[8769])).
% 1.96/2.14 tff(8771,plain,
% 1.96/2.14 ((~b(s(z), s(s(s(s(elem!1)))))) <=> (~b(s(z), elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8770])).
% 1.96/2.14 tff(8772,plain,
% 1.96/2.14 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8752])).
% 1.96/2.14 tff(8773,plain,
% 1.96/2.14 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7316, 8772])).
% 1.96/2.14 tff(8774,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8775,plain,
% 1.96/2.14 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8776,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8775])).
% 1.96/2.14 tff(8777,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8776, 8774])).
% 1.96/2.14 tff(8778,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8779,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8778, 8777])).
% 1.96/2.14 tff(8780,plain,
% 1.96/2.14 ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8779, 245, 7316, 8706, 10])).
% 1.96/2.14 tff(8781,plain,
% 1.96/2.14 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8780, 8732])).
% 1.96/2.14 tff(8782,plain,
% 1.96/2.14 (r(elem!1, z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8752])).
% 1.96/2.14 tff(8783,plain,
% 1.96/2.14 (r(s(s(s(s(elem!1)))), z)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8702, 8782])).
% 1.96/2.14 tff(8784,plain,
% 1.96/2.14 (~r(z, elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6179, 8783, 7316, 10, 8751, 8753, 9, 8759, 8702])).
% 1.96/2.14 tff(8785,plain,
% 1.96/2.14 (b(z, elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[175, 8784, 118])).
% 1.96/2.14 tff(8786,plain,
% 1.96/2.14 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4818, 8785, 8702, 8781])).
% 1.96/2.14 tff(8787,plain,
% 1.96/2.14 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8751])).
% 1.96/2.14 tff(8788,plain,
% 1.96/2.14 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8787])).
% 1.96/2.14 tff(8789,plain,
% 1.96/2.14 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[10, 8788])).
% 1.96/2.14 tff(8790,plain,
% 1.96/2.14 (~r(s(z), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4183, 8783, 1355, 8704, 8789, 8706])).
% 1.96/2.14 tff(8791,plain,
% 1.96/2.14 (b(s(z), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[232, 8790])).
% 1.96/2.14 tff(8792,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(z), z)) | (~b(s(z), 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(X0, 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(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8793,plain,
% 1.96/2.15 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~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)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8794,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~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(X0, 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(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8793])).
% 1.96/2.15 tff(8795,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~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(X0, 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(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8794, 8792])).
% 1.96/2.15 tff(8796,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8797,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8796, 8795])).
% 1.96/2.15 tff(8798,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8797, 245, 355, 2197, 556, 10, 3380])).
% 1.96/2.15 tff(8799,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8800,plain,
% 1.96/2.15 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8799, 8791, 8786, 8773, 10])).
% 1.96/2.15 tff(8801,plain,
% 1.96/2.15 (~b(s(z), elem!1)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8800, 8771])).
% 1.96/2.15 tff(8802,plain,
% 1.96/2.15 (r(s(z), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[389, 8801, 8768])).
% 1.96/2.15 tff(8803,plain,
% 1.96/2.15 (r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8802, 8764])).
% 1.96/2.15 tff(8804,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8752])).
% 1.96/2.15 tff(8805,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8752])).
% 1.96/2.15 tff(8806,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.15 inference(symmetry,[status(thm)],[8805])).
% 1.96/2.15 tff(8807,plain,
% 1.96/2.15 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8806])).
% 1.96/2.15 tff(8808,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.96/2.15 tff(8809,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8810,plain,
% 1.96/2.15 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8811,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8810])).
% 1.96/2.15 tff(8812,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8811, 8809])).
% 1.96/2.15 tff(8813,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8814,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8813, 8812])).
% 1.96/2.15 tff(8815,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8814, 245, 2197, 556, 10, 919, 8808])).
% 1.96/2.15 tff(8816,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8817,plain,
% 1.96/2.15 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8816, 8786, 8773, 10, 8761])).
% 1.96/2.15 tff(8818,plain,
% 1.96/2.15 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8817, 8807])).
% 1.96/2.15 tff(8819,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[787, 8818, 8757])).
% 1.96/2.15 tff(8820,plain,
% 1.96/2.15 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8819, 8804])).
% 1.96/2.15 tff(8821,plain,
% 1.96/2.15 (~r(s(s(s(s(s(z))))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8375, 141, 8820, 8803])).
% 1.96/2.15 tff(8822,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[809, 8821])).
% 1.96/2.15 tff(8823,plain,
% 1.96/2.15 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8762])).
% 1.96/2.15 tff(8824,plain,
% 1.96/2.15 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8823])).
% 1.96/2.15 tff(8825,plain,
% 1.96/2.15 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(symmetry,[status(thm)],[8824])).
% 1.96/2.15 tff(8826,plain,
% 1.96/2.15 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8773, 8825])).
% 1.96/2.15 tff(8827,plain,
% 1.96/2.15 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(elem!1), s(z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8823])).
% 1.96/2.15 tff(8828,plain,
% 1.96/2.15 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 1.96/2.15 inference(symmetry,[status(thm)],[8827])).
% 1.96/2.15 tff(8829,plain,
% 1.96/2.15 (~b(z, s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[2365, 245, 8786, 8773, 10])).
% 1.96/2.15 tff(8830,plain,
% 1.96/2.15 (r(z, s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[644, 8829])).
% 1.96/2.15 tff(8831,plain,
% 1.96/2.15 (~(s(elem!1) = s(s(s(z))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7266, 8753])).
% 1.96/2.15 tff(8832,plain,
% 1.96/2.15 (~(s(s(s(z))) = elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[5452, 8753])).
% 1.96/2.15 tff(8833,plain,
% 1.96/2.15 (~r(s(z), s(s(s(s(s(z))))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[2649, 8802, 8819])).
% 1.96/2.15 tff(8834,plain,
% 1.96/2.15 (b(s(z), s(s(s(s(s(z))))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1698, 8833])).
% 1.96/2.15 tff(8835,plain,
% 1.96/2.15 (~r(s(s(s(z))), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8453, 8834, 8752, 8820, 8802])).
% 1.96/2.15 tff(8836,plain,
% 1.96/2.15 (b(s(s(s(z))), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7257, 8835, 8832])).
% 1.96/2.15 tff(8837,plain,
% 1.96/2.15 (~b(s(elem!1), s(s(s(z))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8464, 8836, 8704, 8706, 7316])).
% 1.96/2.15 tff(8838,plain,
% 1.96/2.15 (r(s(elem!1), s(s(s(z))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8469, 8837, 8831])).
% 1.96/2.15 tff(8839,plain,
% 1.96/2.15 (~r(s(elem!1), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8585, 8822, 8791, 8838, 8786, 8830])).
% 1.96/2.15 tff(8840,plain,
% 1.96/2.15 (b(s(elem!1), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[369, 8839, 348])).
% 1.96/2.15 tff(8841,plain,
% 1.96/2.15 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8840, 8828])).
% 1.96/2.15 tff(8842,plain,
% 1.96/2.15 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), elem!1)),
% 1.96/2.15 inference(monotonicity,[status(thm)],[6408])).
% 1.96/2.15 tff(8843,plain,
% 1.96/2.15 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(symmetry,[status(thm)],[8842])).
% 1.96/2.15 tff(8844,plain,
% 1.96/2.15 (s(z) = s(s(s(s(elem!1))))),
% 1.96/2.15 inference(symmetry,[status(thm)],[204])).
% 1.96/2.15 tff(8845,plain,
% 1.96/2.15 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8844])).
% 1.96/2.15 tff(8846,plain,
% 1.96/2.15 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.96/2.15 inference(symmetry,[status(thm)],[8845])).
% 1.96/2.15 tff(8847,plain,
% 1.96/2.15 (s(s(s(s(s(s(s(elem!1))))))) = z),
% 1.96/2.15 inference(transitivity,[status(thm)],[6651, 206, 8846, 52])).
% 1.96/2.15 tff(8848,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6681, 8847])).
% 1.96/2.15 tff(8849,plain,((~(s(s(s(s(elem!1)))) = s(z))) | (~(elem!1 = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8850,plain,
% 1.96/2.15 (~(s(s(s(s(elem!1)))) = s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8849, 422])).
% 1.96/2.15 tff(8851,plain,
% 1.96/2.15 (~(s(z) = elem!1)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8850, 8626])).
% 1.96/2.15 tff(8852,plain,
% 1.96/2.15 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4226, 106, 1449])).
% 1.96/2.15 tff(8853,plain,
% 1.96/2.15 (b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[215, 32, 8852, 8850])).
% 1.96/2.15 tff(8854,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8855,plain,
% 1.96/2.15 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8856,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8855])).
% 1.96/2.15 tff(8857,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8856, 8854])).
% 1.96/2.15 tff(8858,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8859,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8858, 8857])).
% 1.96/2.15 tff(8860,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8859, 245, 355, 2197, 1596, 2657, 2653])).
% 1.96/2.15 tff(8861,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, 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(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8862,plain,
% 1.96/2.15 (~b(s(z), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8861, 8853, 2197, 1596, 2657])).
% 1.96/2.15 tff(8863,plain,
% 1.96/2.15 (r(s(z), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[232, 8862])).
% 1.96/2.15 tff(8864,plain,
% 1.96/2.15 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3376, 141, 8863, 106])).
% 1.96/2.15 tff(8865,plain,
% 1.96/2.15 (~r(s(z), elem!1)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8864, 8628])).
% 1.96/2.15 tff(8866,plain,
% 1.96/2.15 (b(s(z), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[389, 8865, 8851])).
% 1.96/2.15 tff(8867,plain,
% 1.96/2.15 (b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8866, 8843])).
% 1.96/2.15 tff(8868,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8869,plain,
% 1.96/2.15 (((~b(s(z), 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(elem!1)))), s(z))) | (~b(s(z), 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(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8870,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(elem!1)))), s(z))) | (~b(s(z), 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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8869])).
% 1.96/2.15 tff(8871,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(elem!1)))), s(z))) | (~b(s(z), 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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8870, 8868])).
% 1.96/2.15 tff(8872,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(elem!1)))), s(z))) | (~b(s(z), 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(z))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8873,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8872, 8871])).
% 1.96/2.15 tff(8874,plain,
% 1.96/2.15 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8873, 245, 1596, 2657, 8853])).
% 1.96/2.15 tff(8875,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8874, 8867])).
% 1.96/2.15 tff(8876,plain,((~r(s(s(s(s(elem!1)))), z)) | (~(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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8877,plain,
% 1.96/2.15 (~r(z, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8876, 8841, 8752, 8826, 8783, 8786])).
% 1.96/2.15 tff(8878,plain,
% 1.96/2.15 (b(z, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1421, 8877])).
% 1.96/2.15 tff(8879,plain,
% 1.96/2.15 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8880,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8879])).
% 1.96/2.15 tff(8881,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8880, 5952])).
% 1.96/2.15 tff(8882,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8883,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8882, 8881])).
% 1.96/2.15 tff(8884,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8883, 245, 8791, 8878, 8822, 8761])).
% 1.96/2.15 tff(8885,plain,(b(s(s(s(s(elem!1)))), elem!1) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8886,plain,
% 1.96/2.15 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8885, 10, 9, 1355, 1])).
% 1.96/2.15 tff(8887,plain,
% 1.96/2.15 (~b(elem!1, s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7334, 8886, 7316, 10])).
% 1.96/2.15 tff(8888,plain,
% 1.96/2.15 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3318, 2101, 2824, 1427])).
% 1.96/2.15 tff(8889,plain,
% 1.96/2.15 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1239, 8888, 1304])).
% 1.96/2.15 tff(8890,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8891,plain,
% 1.96/2.15 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8892,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8891])).
% 1.96/2.15 tff(8893,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8892, 8890])).
% 1.96/2.15 tff(8894,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8895,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8894, 8893])).
% 1.96/2.15 tff(8896,plain,
% 1.96/2.15 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8895, 245, 7316, 1427, 2101, 2824])).
% 1.96/2.15 tff(8897,plain,
% 1.96/2.15 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1263, 8896, 1])).
% 1.96/2.15 tff(8898,plain,
% 1.96/2.15 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8712, 245, 7316, 1427, 2101])).
% 1.96/2.15 tff(8899,plain,
% 1.96/2.15 (r(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[353, 8898, 11])).
% 1.96/2.15 tff(8900,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[2377, 8899, 8897, 8889])).
% 1.96/2.15 tff(8901,plain,((~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(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))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8902,plain,
% 1.96/2.15 (s(s(s(elem!1))) = s(elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8901, 8886, 1, 8706, 8704])).
% 1.96/2.15 tff(8903,plain,
% 1.96/2.15 (elem!1 = s(s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1957, 8902])).
% 1.96/2.15 tff(8904,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[428, 8903, 8887, 10])).
% 1.96/2.15 tff(8905,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8906,plain,
% 1.96/2.15 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8905, 7695, 1, 38])).
% 1.96/2.15 tff(8907,plain,
% 1.96/2.15 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[420, 8906, 7])).
% 1.96/2.15 tff(8908,plain,
% 1.96/2.15 (r(elem!1, s(elem!1))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[406, 8533])).
% 1.96/2.15 tff(8909,plain,
% 1.96/2.15 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(elem!1)))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8530])).
% 1.96/2.16 tff(8910,plain,
% 1.96/2.16 (~r(elem!1, s(elem!1))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[1719, 8909])).
% 1.96/2.16 tff(8911,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8910, 8908])).
% 1.96/2.16 tff(8912,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8913,plain,
% 1.96/2.16 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8912, 8907, 8701])).
% 1.96/2.16 tff(8914,plain,
% 1.96/2.16 (~r(s(s(s(elem!1))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2041, 141, 8700, 38])).
% 1.96/2.16 tff(8915,plain,
% 1.96/2.16 (b(s(s(s(elem!1))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[110, 8914, 96])).
% 1.96/2.16 tff(8916,plain,
% 1.96/2.16 (b(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1724, 8701, 1673])).
% 1.96/2.16 tff(8917,plain,
% 1.96/2.16 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8901, 8913, 1, 8916, 8915])).
% 1.96/2.16 tff(8918,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8750, 8917, 8913, 1, 7695, 38])).
% 1.96/2.16 tff(8919,plain,(b(s(s(s(elem!1))), z) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8920,plain,
% 1.96/2.16 (b(s(s(s(elem!1))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8919, 1])).
% 1.96/2.16 tff(8921,plain,
% 1.96/2.16 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[151, 7790, 8])).
% 1.96/2.16 tff(8922,plain,
% 1.96/2.16 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1315, 141, 111, 130])).
% 1.96/2.16 tff(8923,plain,
% 1.96/2.16 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1320, 8922, 1312])).
% 1.96/2.16 tff(8924,plain,
% 1.96/2.16 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2772, 2070, 130, 11, 1312, 10, 1367])).
% 1.96/2.16 tff(8925,plain,
% 1.96/2.16 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1263, 8924, 1])).
% 1.96/2.16 tff(8926,plain,
% 1.96/2.16 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1376, 8925, 1367])).
% 1.96/2.16 tff(8927,plain,
% 1.96/2.16 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1432, 8926, 399])).
% 1.96/2.16 tff(8928,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1396, 245, 2764, 8927, 7316, 1276, 10])).
% 1.96/2.16 tff(8929,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8930,plain,
% 1.96/2.16 (~r(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8929, 1367, 10, 399, 1276, 1, 11, 130])).
% 1.96/2.16 tff(8931,plain,
% 1.96/2.16 (b(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1724, 8930, 1673])).
% 1.96/2.16 tff(8932,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8933,plain,
% 1.96/2.16 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8934,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(X0, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8933])).
% 1.96/2.16 tff(8935,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(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(X0, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8934, 8932])).
% 1.96/2.16 tff(8936,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8937,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8936, 8935])).
% 1.96/2.16 tff(8938,plain,
% 1.96/2.16 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8937, 245, 8931, 1528, 1276])).
% 1.96/2.16 tff(8939,plain,
% 1.96/2.16 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1432, 8938, 399])).
% 1.96/2.16 tff(8940,plain,
% 1.96/2.16 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1376, 8939, 1367])).
% 1.96/2.16 tff(8941,plain,
% 1.96/2.16 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1263, 8940, 1])).
% 1.96/2.16 tff(8942,plain,
% 1.96/2.16 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[5214, 131, 1368])).
% 1.96/2.16 tff(8943,plain,
% 1.96/2.16 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2558, 8942])).
% 1.96/2.16 tff(8944,plain,
% 1.96/2.16 (~r(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4639, 131, 1367])).
% 1.96/2.16 tff(8945,plain,
% 1.96/2.16 (b(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[644, 8944])).
% 1.96/2.16 tff(8946,plain,
% 1.96/2.16 (~r(s(elem!1), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1082, 131, 1367])).
% 1.96/2.16 tff(8947,plain,
% 1.96/2.16 (b(s(elem!1), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[653, 32, 638, 8946])).
% 1.96/2.16 tff(8948,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8949,plain,
% 1.96/2.16 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8950,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8949])).
% 1.96/2.16 tff(8951,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8950, 8948])).
% 1.96/2.16 tff(8952,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8953,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8952, 8951])).
% 1.96/2.16 tff(8954,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8953, 245, 308, 8947, 8945, 556, 8943])).
% 1.96/2.16 tff(8955,plain,((~r(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8956,plain,
% 1.96/2.16 (~r(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8955, 8941, 7316, 1367, 8939])).
% 1.96/2.16 tff(8957,plain,
% 1.96/2.16 (b(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[128, 8956, 124])).
% 1.96/2.16 tff(8958,plain,
% 1.96/2.16 (~b(z, elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8118, 8957, 7316, 7790, 1, 9, 11])).
% 1.96/2.16 tff(8959,plain,
% 1.96/2.16 (r(z, elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[175, 8958, 118])).
% 1.96/2.16 tff(8960,plain,
% 1.96/2.16 (~r(z, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3688, 8959, 8939])).
% 1.96/2.16 tff(8961,plain,
% 1.96/2.16 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1992, 8960])).
% 1.96/2.16 tff(8962,plain,
% 1.96/2.16 (~r(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8291, 8959, 1367])).
% 1.96/2.16 tff(8963,plain,
% 1.96/2.16 (b(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[644, 8962])).
% 1.96/2.16 tff(8964,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8965,plain,
% 1.96/2.16 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8966,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8965])).
% 1.96/2.16 tff(8967,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8966, 8964])).
% 1.96/2.16 tff(8968,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8969,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8968, 8967])).
% 1.96/2.16 tff(8970,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8969, 245, 8963, 8961, 8941, 1528, 1276])).
% 1.96/2.16 tff(8971,plain,((~r(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(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8972,plain,
% 1.96/2.16 (~r(elem!1, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8971, 8923, 2322, 1, 9, 11, 399, 10, 130])).
% 1.96/2.16 tff(8973,plain,
% 1.96/2.16 (b(elem!1, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2777, 8972, 2563])).
% 1.96/2.16 tff(8974,plain,
% 1.96/2.16 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1830, 245, 7316, 8973, 10])).
% 1.96/2.16 tff(8975,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8976,plain,
% 1.96/2.16 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8977,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8976])).
% 1.96/2.16 tff(8978,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8977, 8975])).
% 1.96/2.16 tff(8979,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8980,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8979, 8978])).
% 1.96/2.16 tff(8981,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8980, 245, 234, 2197, 1528, 1276])).
% 1.96/2.16 tff(8982,plain,((~b(z, s(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(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8983,plain,
% 1.96/2.16 (~b(z, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8982, 8923, 8920, 2322])).
% 1.96/2.16 tff(8984,plain,
% 1.96/2.16 (r(z, s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1992, 8983])).
% 1.96/2.16 tff(8985,plain,
% 1.96/2.16 (~r(z, elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1982, 8984, 130])).
% 1.96/2.16 tff(8986,plain,
% 1.96/2.16 (b(z, elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[175, 8985, 118])).
% 1.96/2.16 tff(8987,plain,
% 1.96/2.16 (~r(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4818, 8986, 8983, 8974])).
% 1.96/2.16 tff(8988,plain,
% 1.96/2.16 (~b(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8118, 8986, 7316, 7790, 1, 9, 11])).
% 1.96/2.16 tff(8989,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[128, 8988, 8987, 124])).
% 1.96/2.16 tff(8990,plain,(b(s(s(s(elem!1))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8991,plain,
% 1.96/2.16 (b(s(s(s(elem!1))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8990, 8921, 9, 11, 1, 10, 399])).
% 1.96/2.16 tff(8992,plain,
% 1.96/2.16 (~r(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8731, 5568, 8, 1, 10, 426, 1427])).
% 1.96/2.16 tff(8993,plain,
% 1.96/2.16 (b(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[128, 8992, 3641])).
% 1.96/2.16 tff(8994,plain,
% 1.96/2.16 (~b(z, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4562, 8993, 8920, 1427])).
% 1.96/2.16 tff(8995,plain,
% 1.96/2.16 (r(z, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[197, 8994])).
% 1.96/2.16 tff(8996,plain,
% 1.96/2.16 (~r(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8223, 8995, 7726])).
% 1.96/2.16 tff(8997,plain,
% 1.96/2.16 (b(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[644, 8996])).
% 1.96/2.16 tff(8998,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8999,plain,
% 1.96/2.16 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(9000,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8999])).
% 1.96/2.16 tff(9001,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[9000, 8998])).
% 1.96/2.16 tff(9002,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(9003,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[9002, 9001])).
% 1.96/2.16 tff(9004,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[9003, 245, 8993, 7316, 1427, 8920, 8997])).
% 1.96/2.16 tff(9005,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | b(elem!1, s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(9006,plain,
% 1.96/2.16 (b(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[9005, 426, 124, 8, 1, 10, 8991, 11])).
% 1.96/2.16 tff(9007,plain,
% 1.96/2.16 (r(elem!1, z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[128, 89, 124])).
% 1.96/2.16 tff(9008,plain,
% 1.96/2.16 (~r(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4639, 9007, 1367])).
% 1.96/2.16 tff(9009,plain,
% 1.96/2.16 (b(z, s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[644, 9008])).
% 1.96/2.16 tff(9010,plain,
% 1.96/2.16 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[146, 9007, 8921])).
% 1.96/2.16 tff(9011,plain,
% 1.96/2.16 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2558, 9010])).
% 1.96/2.16 tff(9012,plain,
% 1.96/2.16 (~r(s(elem!1), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1082, 9007, 1367])).
% 1.96/2.16 tff(9013,plain,
% 1.96/2.16 (b(s(elem!1), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1039, 9012])).
% 1.96/2.16 tff(9014,plain,
% 1.96/2.16 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[3304, 9013, 9011, 9009])).
% 1.96/2.16 tff(9015,plain,
% 1.96/2.16 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1263, 9014, 1])).
% 1.96/2.16 tff(9016,plain,
% 1.96/2.16 (b(z, elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8737, 89, 9, 1, 8])).
% 1.96/2.16 tff(9017,plain,
% 1.96/2.16 (~b(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4409, 9016, 8920, 8991, 1287])).
% 1.96/2.16 tff(9018,plain,
% 1.96/2.16 (r(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1724, 9017, 1673])).
% 1.96/2.16 tff(9019,plain,
% 1.96/2.16 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8929, 9018, 10, 399, 1367, 1, 11, 8921])).
% 1.96/2.16 tff(9020,plain,
% 1.96/2.16 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1239, 9019, 1304])).
% 1.96/2.16 tff(9021,plain,
% 1.96/2.16 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2377, 1366, 407])).
% 1.96/2.16 tff(9022,plain,
% 1.96/2.16 (b(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[353, 9021, 11])).
% 1.96/2.16 tff(9023,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(9024,plain,
% 1.96/2.16 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(9025,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[9024])).
% 1.96/2.16 tff(9026,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9025, 9023])).
% 1.96/2.17 tff(9027,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(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))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9028,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9027, 9026])).
% 1.96/2.17 tff(9029,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9028, 245, 9022, 1433, 308, 1427, 10])).
% 1.96/2.17 tff(9030,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9031,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9030, 9020, 9015, 8991, 10, 11, 399, 7316, 1367])).
% 1.96/2.17 tff(9032,plain,(b(elem!1, z) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(z) = s(elem!1)) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9033,plain,
% 1.96/2.17 (b(elem!1, z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9032, 8715, 11, 399, 10, 1, 9006, 9, 8])).
% 1.96/2.17 tff(9034,plain,
% 1.96/2.17 (~b(z, elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8118, 9033, 7316, 7790, 1, 9, 11])).
% 1.96/2.17 tff(9035,plain,
% 1.96/2.17 (r(z, elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[175, 9034, 118])).
% 1.96/2.17 tff(9036,plain,
% 1.96/2.17 (~b(z, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8281, 9033, 9006, 7316, 8991])).
% 1.96/2.17 tff(9037,plain,
% 1.96/2.17 (r(z, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[644, 9036])).
% 1.96/2.17 tff(9038,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8291, 9037, 9035, 8715])).
% 1.96/2.17 tff(9039,plain,(b(elem!1, s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9040,plain,
% 1.96/2.17 (b(elem!1, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9039, 399, 9, 11, 1, 10, 8])).
% 1.96/2.17 tff(9041,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9042,plain,
% 1.96/2.17 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9043,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9042])).
% 1.96/2.17 tff(9044,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9043, 9041])).
% 1.96/2.17 tff(9045,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9046,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9045, 9044])).
% 1.96/2.17 tff(9047,plain,
% 1.96/2.17 (~b(elem!1, z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9046, 245, 7316, 1103, 838])).
% 1.96/2.17 tff(9048,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(elem!1))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9049,plain,
% 1.96/2.17 (((~b(elem!1, s(elem!1))) | (~b(z, 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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9050,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, 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(z, s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9049])).
% 1.96/2.17 tff(9051,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(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(X0, 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(z, s(elem!1))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9050, 9048])).
% 1.96/2.17 tff(9052,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9053,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9052, 9051])).
% 1.96/2.17 tff(9054,plain,
% 1.96/2.17 (~b(z, elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9053, 245, 7316, 1103, 838])).
% 1.96/2.17 tff(9055,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8737, 9054, 9047, 9, 1, 8])).
% 1.96/2.17 tff(9056,plain,((~b(z, s(elem!1))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9057,plain,
% 1.96/2.17 (~b(z, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9056, 9040, 1, 8, 9])).
% 1.96/2.17 tff(9058,plain,
% 1.96/2.17 (r(z, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[644, 9057])).
% 1.96/2.17 tff(9059,plain,
% 1.96/2.17 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2023, 245, 7316, 8991, 9040])).
% 1.96/2.17 tff(9060,plain,
% 1.96/2.17 (r(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[353, 9059, 11])).
% 1.96/2.17 tff(9061,plain,
% 1.96/2.17 (~r(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8223, 9060, 9058])).
% 1.96/2.17 tff(9062,plain,
% 1.96/2.17 (b(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[197, 9061])).
% 1.96/2.17 tff(9063,plain,
% 1.96/2.17 (~b(elem!1, z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4562, 9062, 8920, 8991])).
% 1.96/2.17 tff(9064,plain,
% 1.96/2.17 (b(z, elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8737, 9063, 9, 1, 8])).
% 1.96/2.17 tff(9065,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9066,plain,
% 1.96/2.17 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(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))), z)) | (~b(z, elem!1)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9067,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9066])).
% 1.96/2.17 tff(9068,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9067, 9065])).
% 1.96/2.17 tff(9069,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9070,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9069, 9068])).
% 1.96/2.17 tff(9071,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9070, 245, 9064, 7316, 8991, 9040, 8920])).
% 1.96/2.17 tff(9072,plain,((elem!1 = s(s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9073,plain,
% 1.96/2.17 (elem!1 = s(s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9072, 11, 1, 8, 9, 10])).
% 1.96/2.17 tff(9074,plain,
% 1.96/2.17 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9073])).
% 1.96/2.17 tff(9075,plain,
% 1.96/2.17 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9074])).
% 1.96/2.17 tff(9076,plain,
% 1.96/2.17 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9075])).
% 1.96/2.17 tff(9077,plain,
% 1.96/2.17 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 1.96/2.17 inference(symmetry,[status(thm)],[9076])).
% 1.96/2.17 tff(9078,plain,
% 1.96/2.17 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9077])).
% 1.96/2.17 tff(9079,plain,
% 1.96/2.17 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[9078])).
% 1.96/2.17 tff(9080,plain,
% 1.96/2.17 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9073])).
% 1.96/2.17 tff(9081,plain,
% 1.96/2.17 (b(elem!1, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[428, 9073, 10])).
% 1.96/2.17 tff(9082,plain,
% 1.96/2.17 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.96/2.17 inference(symmetry,[status(thm)],[9074])).
% 1.96/2.17 tff(9083,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9082])).
% 1.96/2.17 tff(9084,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[9083])).
% 1.96/2.17 tff(9085,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[10, 9084])).
% 1.96/2.17 tff(9086,plain,
% 1.96/2.17 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(commutativity,[status(thm)],[])).
% 1.96/2.17 tff(9087,plain,
% 1.96/2.17 ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6648])).
% 1.96/2.17 tff(9088,plain,
% 1.96/2.17 ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9087, 9086])).
% 1.96/2.17 tff(9089,plain,
% 1.96/2.17 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[9088])).
% 1.96/2.17 tff(9090,plain,
% 1.96/2.17 ((~(s(elem!1) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9089])).
% 1.96/2.17 tff(9091,plain,
% 1.96/2.17 (s(s(s(s(elem!1)))) = elem!1),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2567, 422])).
% 1.96/2.17 tff(9092,plain,
% 1.96/2.17 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1065, 9091, 9])).
% 1.96/2.17 tff(9093,plain,
% 1.96/2.17 (~(s(s(s(s(s(z))))) = s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9092, 9090])).
% 1.96/2.17 tff(9094,plain,
% 1.96/2.17 (b(s(s(s(s(s(s(s(elem!1))))))), z) <=> b(s(s(s(elem!1))), z)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6651])).
% 1.96/2.17 tff(9095,plain,
% 1.96/2.17 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 1.96/2.17 inference(symmetry,[status(thm)],[9094])).
% 1.96/2.17 tff(9096,plain,
% 1.96/2.17 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8920, 9095])).
% 1.96/2.17 tff(9097,plain,
% 1.96/2.17 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6872, 9091])).
% 1.96/2.17 tff(9098,plain,
% 1.96/2.17 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8176, 9097])).
% 1.96/2.17 tff(9099,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[422])).
% 1.96/2.17 tff(9100,plain,
% 1.96/2.17 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1051, 9091])).
% 1.96/2.17 tff(9101,plain,
% 1.96/2.17 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[775, 9100])).
% 1.96/2.17 tff(9102,plain,
% 1.96/2.17 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[422])).
% 1.96/2.17 tff(9103,plain,
% 1.96/2.17 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.17 inference(symmetry,[status(thm)],[9102])).
% 1.96/2.17 tff(9104,plain,
% 1.96/2.17 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9103])).
% 1.96/2.17 tff(9105,plain,
% 1.96/2.17 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6647])).
% 1.96/2.17 tff(9106,plain,
% 1.96/2.17 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[422])).
% 1.96/2.17 tff(9107,plain,
% 1.96/2.17 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7316, 9106])).
% 1.96/2.17 tff(9108,plain,
% 1.96/2.17 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9107, 9105])).
% 1.96/2.17 tff(9109,plain,
% 1.96/2.17 (r(z, s(elem!1)) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6647])).
% 1.96/2.17 tff(9110,plain,
% 1.96/2.17 (~b(z, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9056, 1103, 1, 8, 9])).
% 1.96/2.17 tff(9111,plain,
% 1.96/2.17 (r(z, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[644, 9110])).
% 1.96/2.17 tff(9112,plain,
% 1.96/2.17 (r(z, s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9111, 9109])).
% 1.96/2.17 tff(9113,plain,
% 1.96/2.17 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[422])).
% 1.96/2.17 tff(9114,plain,
% 1.96/2.17 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[422])).
% 1.96/2.17 tff(9115,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[9114])).
% 1.96/2.17 tff(9116,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6651])).
% 1.96/2.17 tff(9117,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9116, 9115])).
% 1.96/2.17 tff(9118,plain,
% 1.96/2.17 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9117])).
% 1.96/2.17 tff(9119,plain,
% 1.96/2.17 (b(s(z), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6651])).
% 1.96/2.17 tff(9120,plain,
% 1.96/2.17 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[9119])).
% 1.96/2.17 tff(9121,plain,
% 1.96/2.17 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6650, 6647])).
% 1.96/2.17 tff(9122,plain,
% 1.96/2.17 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[371, 9121])).
% 1.96/2.17 tff(9123,plain,
% 1.96/2.17 (b(z, s(s(s(s(s(s(s(elem!1)))))))) <=> b(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6651])).
% 1.96/2.17 tff(9124,plain,
% 1.96/2.17 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[9123])).
% 1.96/2.17 tff(9125,plain,
% 1.96/2.17 (~r(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8223, 371, 9111])).
% 1.96/2.17 tff(9126,plain,
% 1.96/2.17 (b(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[197, 9125])).
% 1.96/2.17 tff(9127,plain,
% 1.96/2.17 (b(z, s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9126, 9124])).
% 1.96/2.17 tff(9128,assumption,(b(z, s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 1.96/2.17 tff(9129,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.96/2.17 tff(9130,assumption,(r(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.96/2.17 tff(9131,plain,
% 1.96/2.17 (((~![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(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9132,plain,
% 1.96/2.17 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9133,plain,
% 1.96/2.17 (((~![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(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9132])).
% 1.96/2.17 tff(9134,plain,
% 1.96/2.17 (((~![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(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9133, 9131])).
% 1.96/2.17 tff(9135,plain,
% 1.96/2.17 ((~![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(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9136,plain,
% 1.96/2.17 ((~![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(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9135, 9134])).
% 1.96/2.17 tff(9137,plain,
% 1.96/2.17 (~r(z, s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9136, 141, 9130, 9129])).
% 1.96/2.17 tff(9138,plain,
% 1.96/2.17 (b(z, s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[758, 9137])).
% 1.96/2.17 tff(9139,plain,
% 1.96/2.17 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8176, 673])).
% 1.96/2.17 tff(9140,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.96/2.17 tff(9141,plain,
% 1.96/2.17 (((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9142,plain,
% 1.96/2.17 ((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9143,plain,
% 1.96/2.17 ((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9142, 9141])).
% 1.96/2.17 tff(9144,plain,
% 1.96/2.17 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9143, 141, 9140, 9129])).
% 1.96/2.17 tff(9145,plain,
% 1.96/2.17 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6009, 9144, 9139])).
% 1.96/2.17 tff(9146,plain,
% 1.96/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(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(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9147,plain,
% 1.96/2.17 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9148,plain,
% 1.96/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(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(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9147])).
% 1.96/2.17 tff(9149,plain,
% 1.96/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(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(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9148, 9146])).
% 1.96/2.17 tff(9150,plain,
% 1.96/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9151,plain,
% 1.96/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9150, 9149])).
% 1.96/2.17 tff(9152,plain,
% 1.96/2.17 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9151, 141, 9140, 9129])).
% 1.96/2.17 tff(9153,plain,
% 1.96/2.17 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[797, 9152, 673])).
% 1.96/2.17 tff(9154,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9155,plain,
% 1.96/2.18 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9156,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9155])).
% 1.96/2.18 tff(9157,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9156, 9154])).
% 1.96/2.18 tff(9158,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9159,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9158, 9157])).
% 1.96/2.18 tff(9160,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9159, 245, 9153, 9145, 9138, 9128])).
% 1.96/2.18 tff(9161,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(9162,plain,
% 1.96/2.18 (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9161, 9127, 9097, 9112, 9122])).
% 1.96/2.18 tff(9163,plain,
% 1.96/2.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9164,plain,
% 1.96/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9165,plain,
% 1.96/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9164, 9163])).
% 1.96/2.18 tff(9166,plain,
% 1.96/2.18 ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9165, 32, 9162])).
% 1.96/2.18 tff(9167,plain,
% 1.96/2.18 (b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9166, 9093])).
% 1.96/2.18 tff(9168,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9169,plain,
% 1.96/2.18 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), 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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9170,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(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(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9169])).
% 1.96/2.18 tff(9171,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(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(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9170, 9168])).
% 1.96/2.18 tff(9172,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9173,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9172, 9171])).
% 1.96/2.18 tff(9174,plain,
% 1.96/2.18 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9173, 245, 9108, 7400, 9167])).
% 1.96/2.18 tff(9175,plain,
% 1.96/2.18 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9174, 9104])).
% 1.96/2.18 tff(9176,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[787, 9175, 9101])).
% 1.96/2.18 tff(9177,plain,
% 1.96/2.18 (~r(z, elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[6517, 9176, 9091, 170, 9097])).
% 1.96/2.18 tff(9178,plain,
% 1.96/2.18 (b(z, elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[175, 9177, 118])).
% 1.96/2.18 tff(9179,plain,
% 1.96/2.18 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(elem!1), z)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[6648])).
% 1.96/2.18 tff(9180,plain,
% 1.96/2.18 (b(s(elem!1), z) <=> b(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.18 inference(symmetry,[status(thm)],[9179])).
% 1.96/2.18 tff(9181,plain,
% 1.96/2.18 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[5923, 9092])).
% 1.96/2.18 tff(9182,plain,
% 1.96/2.18 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[6815, 9007, 9097, 170, 9091, 8920, 235])).
% 1.96/2.18 tff(9183,plain,
% 1.96/2.18 (b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[787, 9182, 9101])).
% 1.96/2.18 tff(9184,plain,
% 1.96/2.18 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9183, 9102])).
% 1.96/2.18 tff(9185,plain,
% 1.96/2.18 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[6408])).
% 1.96/2.18 tff(9186,plain,
% 1.96/2.18 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(symmetry,[status(thm)],[9185])).
% 1.96/2.18 tff(9187,plain,
% 1.96/2.18 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9186])).
% 1.96/2.18 tff(9188,plain,
% 1.96/2.18 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[79, 9187])).
% 1.96/2.18 tff(9189,plain,
% 1.96/2.18 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4818, 9007, 9188, 9016])).
% 1.96/2.18 tff(9190,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9191,plain,
% 1.96/2.18 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, 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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9192,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9191])).
% 1.96/2.18 tff(9193,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9192, 9190])).
% 1.96/2.18 tff(9194,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9195,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9194, 9193])).
% 1.96/2.18 tff(9196,plain,
% 1.96/2.18 (~b(s(s(s(s(s(z))))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9195, 245, 9189, 9108, 9184, 7400])).
% 1.96/2.18 tff(9197,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[738, 9196])).
% 1.96/2.18 tff(9198,plain,
% 1.96/2.18 (~r(s(elem!1), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[5942, 9197, 9007, 9101, 9181, 1103, 7316])).
% 1.96/2.18 tff(9199,plain,
% 1.96/2.18 (b(s(elem!1), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1039, 9198])).
% 1.96/2.18 tff(9200,plain,
% 1.96/2.18 (b(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9199, 9180])).
% 1.96/2.18 tff(9201,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9202,plain,
% 1.96/2.18 (((~b(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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, 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))))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9203,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, 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))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9202])).
% 1.96/2.18 tff(9204,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, 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))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9203, 9201])).
% 1.96/2.18 tff(9205,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, 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))))), z)))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9206,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9205, 9204])).
% 1.96/2.18 tff(9207,plain,
% 1.96/2.18 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9206, 245, 9189, 9108, 7400])).
% 1.96/2.18 tff(9208,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9207, 9200])).
% 1.96/2.18 tff(9209,plain,(b(elem!1, z) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(9210,plain,
% 1.96/2.18 (b(elem!1, z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9209, 9126, 1103, 7400, 170, 422, 9, 1, 8])).
% 1.96/2.18 tff(9211,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9176, 9099])).
% 1.96/2.18 tff(9212,plain,
% 1.96/2.18 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[6651])).
% 1.96/2.18 tff(9213,plain,
% 1.96/2.18 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(symmetry,[status(thm)],[9212])).
% 1.96/2.18 tff(9214,plain,
% 1.96/2.18 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[422])).
% 1.96/2.18 tff(9215,plain,
% 1.96/2.18 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9214, 9213])).
% 1.96/2.18 tff(9216,plain,
% 1.96/2.18 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[170, 9215])).
% 1.96/2.18 tff(9217,plain,
% 1.96/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(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(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9218,plain,
% 1.96/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9219,plain,
% 1.96/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9218, 9217])).
% 1.96/2.18 tff(9220,plain,
% 1.96/2.18 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9219, 141, 9216, 9211])).
% 1.96/2.18 tff(9221,plain,
% 1.96/2.18 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[797, 9220, 9097])).
% 1.96/2.18 tff(9222,plain,
% 1.96/2.18 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4808, 9178, 422])).
% 1.96/2.18 tff(9223,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9224,plain,
% 1.96/2.18 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9225,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9224])).
% 1.96/2.18 tff(9226,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9225, 9223])).
% 1.96/2.19 tff(9227,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9228,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9227, 9226])).
% 1.96/2.19 tff(9229,plain,
% 1.96/2.19 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9228, 245, 9222, 7400, 9096, 9167])).
% 1.96/2.19 tff(9230,plain,
% 1.96/2.19 (~b(s(s(s(s(s(z))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9229, 9221])).
% 1.96/2.19 tff(9231,plain,
% 1.96/2.19 (r(s(s(s(s(s(z))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[738, 9230])).
% 1.96/2.19 tff(9232,plain,
% 1.96/2.19 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9210, 9113])).
% 1.96/2.19 tff(9233,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), z)) | (~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(X0, 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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9234,plain,
% 1.96/2.19 (((~b(z, 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(elem!1)))), z)) | (~b(z, 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))))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9235,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9234])).
% 1.96/2.19 tff(9236,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9235, 9233])).
% 1.96/2.19 tff(9237,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9238,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9237, 9236])).
% 1.96/2.19 tff(9239,plain,
% 1.96/2.19 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9238, 245, 9222, 9232, 9108])).
% 1.96/2.19 tff(9240,plain,
% 1.96/2.19 (r(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[6665, 32, 463, 9239])).
% 1.96/2.19 tff(9241,plain,
% 1.96/2.19 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[6648])).
% 1.96/2.19 tff(9242,plain,
% 1.96/2.19 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z))))))),
% 1.96/2.19 inference(symmetry,[status(thm)],[9241])).
% 1.96/2.19 tff(9243,plain,
% 1.96/2.19 ((~(s(elem!1) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9242])).
% 1.96/2.19 tff(9244,plain,
% 1.96/2.19 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(z))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9092, 9243])).
% 1.96/2.19 tff(9245,plain,
% 1.96/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), 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(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9246,plain,
% 1.96/2.19 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9247,plain,
% 1.96/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), 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(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9246])).
% 1.96/2.19 tff(9248,plain,
% 1.96/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), 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(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9247, 9245])).
% 1.96/2.19 tff(9249,plain,
% 1.96/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9250,plain,
% 1.96/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9249, 9248])).
% 1.96/2.19 tff(9251,plain,
% 1.96/2.19 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9250, 141, 9240, 9231])).
% 1.96/2.19 tff(9252,plain,
% 1.96/2.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9253,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9254,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9253, 9252])).
% 1.96/2.19 tff(9255,plain,
% 1.96/2.19 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9254, 32, 9251])).
% 1.96/2.19 tff(9256,plain,
% 1.96/2.19 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9255, 9244])).
% 1.96/2.19 tff(9257,plain,
% 1.96/2.19 (((~![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(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9258,plain,
% 1.96/2.19 ((~![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(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9259,plain,
% 1.96/2.19 ((~![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(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9258, 9257])).
% 1.96/2.19 tff(9260,plain,
% 1.96/2.19 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9259, 141, 9216, 9211])).
% 1.96/2.19 tff(9261,plain,
% 1.96/2.19 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[6009, 9260, 9098])).
% 1.96/2.19 tff(9262,plain,
% 1.96/2.19 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[6647])).
% 1.96/2.19 tff(9263,plain,
% 1.96/2.19 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(elem!1), s(z))),
% 1.96/2.19 inference(symmetry,[status(thm)],[9262])).
% 1.96/2.19 tff(9264,plain,
% 1.96/2.19 ((~b(s(s(s(s(s(elem!1))))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9263])).
% 1.96/2.19 tff(9265,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.96/2.19 tff(9266,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.96/2.19 tff(9267,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 1.96/2.19 tff(9268,plain,
% 1.96/2.19 (~r(s(z), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[5856, 141, 220, 722])).
% 1.96/2.19 tff(9269,plain,
% 1.96/2.19 (b(s(z), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1698, 9268])).
% 1.96/2.19 tff(9270,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9271,plain,
% 1.96/2.19 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9272,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9271])).
% 1.96/2.19 tff(9273,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9272, 9270])).
% 1.96/2.19 tff(9274,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9275,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9274, 9273])).
% 1.96/2.19 tff(9276,plain,
% 1.96/2.19 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9275, 245, 9269, 9267, 9266, 9265])).
% 1.96/2.19 tff(9277,plain,
% 1.96/2.19 (~b(s(elem!1), s(z))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9276, 9264])).
% 1.96/2.19 tff(9278,plain,
% 1.96/2.19 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(elem!1), s(z))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[6648])).
% 1.96/2.19 tff(9279,plain,
% 1.96/2.19 ((~r(s(s(s(s(s(elem!1))))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9278])).
% 1.96/2.19 tff(9280,assumption,(r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.96/2.19 tff(9281,plain,
% 1.96/2.19 (((~![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(elem!1))))), z)) | (~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(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9282,plain,
% 1.96/2.19 ((~![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(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9283,plain,
% 1.96/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9282, 9281])).
% 1.96/2.19 tff(9284,plain,
% 1.96/2.19 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9283, 141, 220, 9280])).
% 1.96/2.19 tff(9285,plain,
% 1.96/2.19 (~r(s(elem!1), s(z))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9284, 9279])).
% 1.96/2.19 tff(9286,plain,
% 1.96/2.19 (b(s(elem!1), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[369, 9285, 358])).
% 1.96/2.19 tff(9287,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9286, 9277])).
% 1.96/2.19 tff(9288,plain,((~r(s(z), z)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(9289,plain,
% 1.96/2.19 (~r(s(z), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9288, 9221, 348, 422, 9261, 9256, 9240, 9231])).
% 1.96/2.19 tff(9290,plain,
% 1.96/2.19 (b(s(z), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[232, 9289])).
% 1.96/2.19 tff(9291,plain,
% 1.96/2.19 (~b(s(z), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4436, 9290, 9210, 9178])).
% 1.96/2.19 tff(9292,plain,
% 1.96/2.19 (r(s(z), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[389, 9291, 8627])).
% 1.96/2.19 tff(9293,plain,
% 1.96/2.19 (~r(s(z), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1143, 9292, 170])).
% 1.96/2.19 tff(9294,plain,
% 1.96/2.19 (b(s(z), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1133, 9293])).
% 1.96/2.19 tff(9295,plain,
% 1.96/2.19 (b(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9294, 9120])).
% 1.96/2.19 tff(9296,plain,
% 1.96/2.19 (~r(s(z), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2649, 9292, 9176])).
% 1.96/2.19 tff(9297,plain,
% 1.96/2.19 (b(s(z), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1698, 9296])).
% 1.96/2.19 tff(9298,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9299,plain,
% 1.96/2.19 (((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9300,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9299])).
% 1.96/2.19 tff(9301,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9300, 9298])).
% 1.96/2.19 tff(9302,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9303,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9302, 9301])).
% 1.96/2.19 tff(9304,plain,
% 1.96/2.19 (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9303, 245, 9290, 9297, 9221, 9261, 9096])).
% 1.96/2.19 tff(9305,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9304, 9295])).
% 1.96/2.19 tff(9306,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(9307,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9306, 170, 422, 7400, 1103, 9, 1, 8])).
% 1.96/2.19 tff(9308,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), s(elem!1))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[353, 9307, 11])).
% 1.96/2.19 tff(9309,plain,
% 1.96/2.19 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9308, 6653])).
% 1.96/2.19 tff(9310,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(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(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(X0, 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(s(elem!1)))), s(s(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(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9311,plain,
% 1.96/2.19 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(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(elem!1)))), s(s(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(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9312,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(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(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(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(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9311])).
% 1.96/2.19 tff(9313,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(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(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(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(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9312, 9310])).
% 1.96/2.19 tff(9314,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(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(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9315,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9314, 9313])).
% 1.96/2.19 tff(9316,plain,
% 1.96/2.19 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9315, 245, 9108, 7400])).
% 1.96/2.19 tff(9317,plain,
% 1.96/2.19 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9316, 9309])).
% 1.96/2.19 tff(9318,plain,
% 1.96/2.19 (~b(elem!1, s(s(s(elem!1))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9317, 9118])).
% 1.96/2.19 tff(9319,plain,
% 1.96/2.19 (r(elem!1, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1724, 9318, 1673])).
% 1.96/2.19 tff(9320,plain,
% 1.96/2.19 (~b(z, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9209, 89, 1103, 7400, 170, 422, 9, 1, 8])).
% 1.96/2.19 tff(9321,plain,
% 1.96/2.19 (~r(z, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3608, 9007, 2070])).
% 2.03/2.20 tff(9322,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[197, 9321, 9320])).
% 2.03/2.20 tff(9323,plain,(b(elem!1, z) | (~r(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(9324,plain,
% 2.03/2.20 (b(elem!1, z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9323, 9319, 1103, 7400, 170, 422, 9, 1, 8])).
% 2.03/2.20 tff(9325,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9324, 9113])).
% 2.03/2.20 tff(9326,plain,
% 2.03/2.20 (~(s(s(s(s(s(z))))) = s(s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[1153, 9090])).
% 2.03/2.20 tff(9327,plain,
% 2.03/2.20 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9328,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), 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(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9327])).
% 2.03/2.20 tff(9329,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), 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(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9328, 9168])).
% 2.03/2.20 tff(9330,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))), 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(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9331,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9330, 9329])).
% 2.03/2.20 tff(9332,plain,
% 2.03/2.20 (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9331, 245, 1596, 8808, 7400])).
% 2.03/2.20 tff(9333,plain,
% 2.03/2.20 ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9165, 32, 9332])).
% 2.03/2.20 tff(9334,plain,
% 2.03/2.20 (r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9333, 9326])).
% 2.03/2.20 tff(9335,plain,
% 2.03/2.20 (((~![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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9336,plain,
% 2.03/2.20 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9337,plain,
% 2.03/2.20 (((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9336])).
% 2.03/2.20 tff(9338,plain,
% 2.03/2.20 (((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9337, 9335])).
% 2.03/2.20 tff(9339,plain,
% 2.03/2.20 ((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9340,plain,
% 2.03/2.20 ((~![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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9339, 9338])).
% 2.03/2.20 tff(9341,plain,
% 2.03/2.20 (~r(s(s(s(s(s(z))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9340, 141, 9130, 9334])).
% 2.03/2.20 tff(9342,plain,
% 2.03/2.20 (b(s(s(s(s(s(z))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[738, 9341])).
% 2.03/2.20 tff(9343,plain,
% 2.03/2.20 (~r(z, s(s(s(s(s(z))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9136, 141, 9130, 9334])).
% 2.03/2.20 tff(9344,plain,
% 2.03/2.20 (b(z, s(s(s(s(s(z))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[758, 9343])).
% 2.03/2.20 tff(9345,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9346,plain,
% 2.03/2.20 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9347,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9346])).
% 2.03/2.20 tff(9348,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9347, 9345])).
% 2.03/2.20 tff(9349,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9350,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9349, 9348])).
% 2.03/2.20 tff(9351,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9350, 245, 1943, 9344, 9342, 8808])).
% 2.03/2.20 tff(9352,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~(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(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(9353,plain,
% 2.03/2.20 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9352, 9325, 9112, 9092, 422, 9108, 7400])).
% 2.03/2.20 tff(9354,plain,
% 2.03/2.20 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9353, 9104])).
% 2.03/2.20 tff(9355,plain,
% 2.03/2.20 (r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[787, 9354, 9101])).
% 2.03/2.20 tff(9356,plain,
% 2.03/2.20 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9355, 9099])).
% 2.03/2.20 tff(9357,plain,
% 2.03/2.20 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9259, 141, 9216, 9356])).
% 2.03/2.20 tff(9358,plain,
% 2.03/2.20 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[6009, 9357, 9098])).
% 2.03/2.20 tff(9359,plain,
% 2.03/2.20 (~r(z, elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[6517, 9355, 9091, 170, 9097])).
% 2.03/2.20 tff(9360,plain,
% 2.03/2.20 (b(z, elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[175, 9359, 118])).
% 2.03/2.20 tff(9361,plain,
% 2.03/2.20 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[4808, 9360, 422])).
% 2.03/2.20 tff(9362,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), z)), introduced(assumption)).
% 2.03/2.20 tff(9363,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9364,plain,
% 2.03/2.20 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9365,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9364])).
% 2.03/2.20 tff(9366,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9365, 9363])).
% 2.03/2.20 tff(9367,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9368,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9367, 9366])).
% 2.03/2.20 tff(9369,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9368, 245, 2197, 1943, 9266, 919, 9362])).
% 2.03/2.20 tff(9370,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(9371,plain,
% 2.03/2.20 (~b(s(s(s(s(s(z))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9370, 9361, 9325, 9358, 9096])).
% 2.03/2.20 tff(9372,plain,
% 2.03/2.20 (r(s(s(s(s(s(z))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[738, 9371])).
% 2.03/2.20 tff(9373,plain,
% 2.03/2.20 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9238, 245, 9361, 9325, 9108])).
% 2.03/2.20 tff(9374,plain,
% 2.03/2.20 (r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[6665, 32, 463, 9373])).
% 2.03/2.20 tff(9375,plain,
% 2.03/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(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(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9376,plain,
% 2.03/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9377,plain,
% 2.03/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9376, 9375])).
% 2.03/2.20 tff(9378,plain,
% 2.03/2.20 (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9377, 141, 9374, 9372])).
% 2.03/2.20 tff(9379,plain,
% 2.03/2.20 ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9165, 32, 9378])).
% 2.03/2.20 tff(9380,plain,
% 2.03/2.20 (b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9379, 9093])).
% 2.03/2.20 tff(9381,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9382,plain,
% 2.03/2.20 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9383,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9382])).
% 2.03/2.20 tff(9384,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9383, 9381])).
% 2.03/2.20 tff(9385,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9386,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9385, 9384])).
% 2.03/2.20 tff(9387,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9386, 245, 9325, 9108, 9358, 9309, 9096, 9380])).
% 2.03/2.20 tff(9388,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(9389,plain,
% 2.03/2.20 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9388, 9073, 9085, 9081, 9, 1, 8, 11])).
% 2.03/2.20 tff(9390,plain,
% 2.03/2.20 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[110, 9389, 96])).
% 2.03/2.20 tff(9391,plain,
% 2.03/2.20 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9390, 9080])).
% 2.03/2.20 tff(9392,plain,
% 2.03/2.20 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9391, 9079])).
% 2.03/2.20 tff(9393,plain,
% 2.03/2.20 (b(z, s(s(s(s(s(s(s(elem!1)))))))) <=> b(z, s(s(s(elem!1))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9077])).
% 2.03/2.20 tff(9394,plain,
% 2.03/2.20 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(symmetry,[status(thm)],[9393])).
% 2.03/2.20 tff(9395,plain,
% 2.03/2.20 (~b(z, s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9056, 9081, 1, 8, 9])).
% 2.03/2.20 tff(9396,plain,
% 2.03/2.20 (r(z, s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[644, 9395])).
% 2.03/2.20 tff(9397,plain,
% 2.03/2.20 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9073])).
% 2.03/2.20 tff(9398,plain,
% 2.03/2.20 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7316, 9397])).
% 2.03/2.20 tff(9399,plain,
% 2.03/2.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2786, 9390, 10, 9398, 9081])).
% 2.03/2.20 tff(9400,plain,
% 2.03/2.20 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[353, 9399, 11])).
% 2.03/2.20 tff(9401,plain,
% 2.03/2.20 (~r(z, s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[8223, 9400, 9396])).
% 2.03/2.20 tff(9402,plain,
% 2.03/2.20 (b(z, s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[197, 9401])).
% 2.03/2.20 tff(9403,plain,
% 2.03/2.20 (b(z, s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9402, 9394])).
% 2.03/2.20 tff(9404,plain,
% 2.03/2.20 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9074])).
% 2.03/2.20 tff(9405,plain,
% 2.03/2.20 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9398, 9404])).
% 2.03/2.20 tff(9406,plain,
% 2.03/2.20 (~b(elem!1, z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[4562, 9402, 8920, 9390])).
% 2.03/2.20 tff(9407,plain,
% 2.03/2.20 (b(z, elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[8737, 9406, 9, 1, 8])).
% 2.03/2.21 tff(9408,plain,
% 2.03/2.21 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4808, 9407, 9073])).
% 2.03/2.21 tff(9409,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(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(s(s(elem!1))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(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(s(s(elem!1))))))), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9410,plain,
% 2.03/2.21 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(s(elem!1)))))))))) <=> ((~b(z, s(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(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(s(s(elem!1))))))), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9411,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, 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(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(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(s(s(elem!1))))))), s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9410])).
% 2.03/2.21 tff(9412,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, 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(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(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(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(s(s(elem!1))))))), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9411, 9409])).
% 2.03/2.21 tff(9413,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, 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(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(s(s(elem!1))))))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9414,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9413, 9412])).
% 2.03/2.21 tff(9415,plain,
% 2.03/2.21 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9414, 245, 9408, 9405, 9085, 9403])).
% 2.03/2.21 tff(9416,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9415, 9392])).
% 2.03/2.21 tff(9417,plain,((s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9418,plain,
% 2.03/2.21 (s(s(s(elem!1))) = s(elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9417, 10, 1, 8, 9])).
% 2.03/2.21 tff(9419,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9418])).
% 2.03/2.21 tff(9420,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[9419])).
% 2.03/2.21 tff(9421,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[10, 9420])).
% 2.03/2.21 tff(9422,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9418])).
% 2.03/2.21 tff(9423,plain,
% 2.03/2.21 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[9422])).
% 2.03/2.21 tff(9424,plain,
% 2.03/2.21 (elem!1 = s(s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1957, 9418])).
% 2.03/2.21 tff(9425,plain,
% 2.03/2.21 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9424])).
% 2.03/2.21 tff(9426,plain,
% 2.03/2.21 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9425, 9423])).
% 2.03/2.21 tff(9427,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7316, 9426])).
% 2.03/2.21 tff(9428,plain,
% 2.03/2.21 (~b(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8982, 9427, 8920, 9421])).
% 2.03/2.21 tff(9429,plain,
% 2.03/2.21 (r(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1992, 9428])).
% 2.03/2.21 tff(9430,plain,
% 2.03/2.21 (s(s(s(s(elem!1)))) = elem!1),
% 2.03/2.21 inference(symmetry,[status(thm)],[9424])).
% 2.03/2.21 tff(9431,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9430])).
% 2.03/2.21 tff(9432,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 2.03/2.21 inference(transitivity,[status(thm)],[9431, 339])).
% 2.03/2.21 tff(9433,plain,
% 2.03/2.21 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9432])).
% 2.03/2.21 tff(9434,plain,
% 2.03/2.21 (~(s(z) = elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[209, 9433])).
% 2.03/2.21 tff(9435,plain,
% 2.03/2.21 (~b(z, elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4808, 9428, 9424])).
% 2.03/2.21 tff(9436,plain,
% 2.03/2.21 (r(z, elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[175, 9435, 118])).
% 2.03/2.21 tff(9437,plain,
% 2.03/2.21 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9418])).
% 2.03/2.21 tff(9438,plain,
% 2.03/2.21 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[9437])).
% 2.03/2.21 tff(9439,plain,
% 2.03/2.21 (b(elem!1, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[428, 9424, 10])).
% 2.03/2.21 tff(9440,plain,
% 2.03/2.21 (~b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9056, 9439, 1, 8, 9])).
% 2.03/2.21 tff(9441,plain,
% 2.03/2.21 (r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[644, 9440])).
% 2.03/2.21 tff(9442,plain,
% 2.03/2.21 (r(z, s(s(s(elem!1))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9441, 9438])).
% 2.03/2.21 tff(9443,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9418])).
% 2.03/2.21 tff(9444,plain,
% 2.03/2.21 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.21 inference(symmetry,[status(thm)],[9443])).
% 2.03/2.21 tff(9445,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7316, 9444])).
% 2.03/2.21 tff(9446,plain,
% 2.03/2.21 (b(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8737, 9435, 9, 1, 8])).
% 2.03/2.21 tff(9447,plain,
% 2.03/2.21 (~b(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[6573, 9446, 9445, 9442, 1673, 9436])).
% 2.03/2.21 tff(9448,plain,
% 2.03/2.21 (r(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[389, 9447, 9434])).
% 2.03/2.21 tff(9449,plain,
% 2.03/2.21 (~r(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[6420, 9448, 9424, 9429])).
% 2.03/2.21 tff(9450,plain,
% 2.03/2.21 (b(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1421, 9449])).
% 2.03/2.21 tff(9451,plain,
% 2.03/2.21 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9424])).
% 2.03/2.21 tff(9452,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9446, 9451])).
% 2.03/2.21 tff(9453,plain,
% 2.03/2.21 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7316, 9425])).
% 2.03/2.21 tff(9454,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9418])).
% 2.03/2.21 tff(9455,plain,
% 2.03/2.21 (b(s(elem!1), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[8920, 9454])).
% 2.03/2.21 tff(9456,plain,
% 2.03/2.21 (b(s(z), z) <=> b(elem!1, z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[2898])).
% 2.03/2.21 tff(9457,plain,
% 2.03/2.21 (b(elem!1, z) <=> b(s(z), z)),
% 2.03/2.21 inference(symmetry,[status(thm)],[9456])).
% 2.03/2.21 tff(9458,plain,
% 2.03/2.21 (b(s(z), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[4186, 9457])).
% 2.03/2.21 tff(9459,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7685, 9458])).
% 2.03/2.21 tff(9460,plain,((~(s(z) = elem!1)) | b(s(z), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9461,plain,
% 2.03/2.21 (~(s(z) = elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9460, 7685, 4186])).
% 2.03/2.21 tff(9462,plain,
% 2.03/2.21 (r(s(z), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[232, 7685])).
% 2.03/2.21 tff(9463,plain,
% 2.03/2.21 (~r(s(z), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8611, 9462, 289])).
% 2.03/2.21 tff(9464,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[389, 9463, 9461, 7680])).
% 2.03/2.21 tff(9465,plain,(b(s(z), z) | b(s(z), elem!1) | (~r(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9466,plain,
% 2.03/2.21 (b(s(z), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9465, 9447, 9436, 9446])).
% 2.03/2.21 tff(9467,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9468,plain,
% 2.03/2.21 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9469,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9468])).
% 2.03/2.21 tff(9470,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9469, 9467])).
% 2.03/2.21 tff(9471,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9472,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9471, 9470])).
% 2.03/2.21 tff(9473,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9472, 245, 9466, 9455, 9453, 9452, 9450])).
% 2.03/2.21 tff(9474,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9475,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9474, 9, 1, 8])).
% 2.03/2.21 tff(9476,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[420, 9475, 7])).
% 2.03/2.21 tff(9477,plain,
% 2.03/2.21 (~r(elem!1, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1384, 8921, 9476])).
% 2.03/2.21 tff(9478,plain,
% 2.03/2.21 (b(elem!1, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2777, 9477, 2563])).
% 2.03/2.21 tff(9479,plain,
% 2.03/2.21 (~b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9056, 9478, 1, 8, 9])).
% 2.03/2.21 tff(9480,plain,
% 2.03/2.21 (r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[644, 9479])).
% 2.03/2.21 tff(9481,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1350, 9480, 9476])).
% 2.03/2.21 tff(9482,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2558, 9481])).
% 2.03/2.21 tff(9483,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2025, 8921, 9476, 2338, 1, 7316])).
% 2.03/2.21 tff(9484,plain,
% 2.03/2.21 (~r(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[3674, 9480, 9476])).
% 2.03/2.21 tff(9485,plain,
% 2.03/2.21 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1992, 9484])).
% 2.03/2.21 tff(9486,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2032, 245, 8920, 9485, 9483, 9482])).
% 2.03/2.21 tff(9487,plain,((elem!1 = s(s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9488,plain,
% 2.03/2.21 (elem!1 = s(s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9487, 9, 8, 1])).
% 2.03/2.21 tff(9489,plain,
% 2.03/2.21 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9490,plain,
% 2.03/2.21 (s(s(s(s(elem!1)))) = elem!1),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2567, 9488])).
% 2.03/2.21 tff(9491,plain,
% 2.03/2.21 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1051, 9490])).
% 2.03/2.21 tff(9492,plain,
% 2.03/2.21 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[775, 9491])).
% 2.03/2.21 tff(9493,plain,
% 2.03/2.21 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9494,plain,
% 2.03/2.21 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.21 inference(symmetry,[status(thm)],[9493])).
% 2.03/2.21 tff(9495,plain,
% 2.03/2.21 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9494])).
% 2.03/2.21 tff(9496,plain,
% 2.03/2.21 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1065, 9490, 9])).
% 2.03/2.21 tff(9497,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9498,plain,
% 2.03/2.21 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9499,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[9498])).
% 2.03/2.21 tff(9500,plain,
% 2.03/2.21 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4808, 9016, 9488])).
% 2.03/2.21 tff(9501,plain,
% 2.03/2.21 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9502,plain,
% 2.03/2.21 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 2.03/2.21 inference(symmetry,[status(thm)],[9501])).
% 2.03/2.21 tff(9503,plain,
% 2.03/2.21 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9501])).
% 2.03/2.21 tff(9504,plain,
% 2.03/2.21 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9503])).
% 2.03/2.21 tff(9505,plain,
% 2.03/2.21 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 2.03/2.21 inference(symmetry,[status(thm)],[9504])).
% 2.03/2.21 tff(9506,plain,
% 2.03/2.21 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9505, 9502])).
% 2.03/2.21 tff(9507,plain,
% 2.03/2.21 ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9506])).
% 2.03/2.21 tff(9508,plain,
% 2.03/2.21 (r(s(elem!1), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9501])).
% 2.03/2.21 tff(9509,plain,
% 2.03/2.21 ((~r(s(elem!1), z)) <=> (~r(s(s(s(s(s(elem!1))))), z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9508])).
% 2.03/2.21 tff(9510,plain,
% 2.03/2.21 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9511,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.03/2.21 inference(symmetry,[status(thm)],[9510])).
% 2.03/2.21 tff(9512,plain,
% 2.03/2.21 (r(elem!1, s(elem!1))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9476, 9511])).
% 2.03/2.21 tff(9513,plain,
% 2.03/2.21 (~r(s(elem!1), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1082, 9007, 9512])).
% 2.03/2.21 tff(9514,plain,
% 2.03/2.21 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9513, 9509])).
% 2.03/2.21 tff(9515,plain,
% 2.03/2.21 (b(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[6665, 32, 463, 9514])).
% 2.03/2.21 tff(9516,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9504])).
% 2.03/2.21 tff(9517,plain,
% 2.03/2.21 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[8920, 9516])).
% 2.03/2.21 tff(9518,plain,
% 2.03/2.21 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9501])).
% 2.03/2.21 tff(9519,plain,
% 2.03/2.21 (~r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4639, 9007, 9512])).
% 2.03/2.21 tff(9520,plain,
% 2.03/2.21 (b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[644, 9519])).
% 2.03/2.21 tff(9521,plain,
% 2.03/2.21 (b(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9520, 9518])).
% 2.03/2.21 tff(9522,plain,
% 2.03/2.21 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9523,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9522])).
% 2.03/2.21 tff(9524,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9523, 6672])).
% 2.03/2.21 tff(9525,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9526,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9525, 9524])).
% 2.03/2.21 tff(9527,plain,
% 2.03/2.21 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9526, 245, 9521, 9517, 9515])).
% 2.03/2.21 tff(9528,plain,
% 2.03/2.21 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9527, 9507])).
% 2.03/2.21 tff(9529,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[353, 9528, 11])).
% 2.03/2.21 tff(9530,plain,
% 2.03/2.21 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[415, 9529, 9476])).
% 2.03/2.21 tff(9531,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1239, 9530, 1304])).
% 2.03/2.21 tff(9532,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8982, 9531, 8920, 9500])).
% 2.03/2.21 tff(9533,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1320, 9532, 1312])).
% 2.03/2.21 tff(9534,plain,
% 2.03/2.21 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9533, 9499])).
% 2.03/2.21 tff(9535,plain,
% 2.03/2.21 (~r(elem!1, s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2762, 9529, 9512])).
% 2.03/2.21 tff(9536,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9535, 9534])).
% 2.03/2.21 tff(9537,plain,(b(elem!1, z) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9538,plain,
% 2.03/2.21 (b(elem!1, z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9537, 11, 9, 1, 8])).
% 2.03/2.21 tff(9539,plain,
% 2.03/2.21 (b(z, elem!1) <=> b(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9540,plain,
% 2.03/2.21 (b(z, s(s(s(s(elem!1))))) <=> b(z, elem!1)),
% 2.03/2.21 inference(symmetry,[status(thm)],[9539])).
% 2.03/2.21 tff(9541,plain,
% 2.03/2.21 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.21 tff(9542,plain,
% 2.03/2.21 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7316, 9541])).
% 2.03/2.21 tff(9543,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[422])).
% 2.03/2.21 tff(9544,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.21 inference(symmetry,[status(thm)],[9543])).
% 2.03/2.21 tff(9545,plain,
% 2.03/2.21 ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[6652])).
% 2.03/2.21 tff(9546,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[6650])).
% 2.03/2.21 tff(9547,plain,
% 2.03/2.21 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[234, 9546])).
% 2.03/2.21 tff(9548,plain,
% 2.03/2.21 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[556, 9105])).
% 2.03/2.21 tff(9549,plain,
% 2.03/2.21 (~r(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[3674, 3526, 406])).
% 2.03/2.21 tff(9550,plain,
% 2.03/2.21 (b(z, s(elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[644, 9549])).
% 2.03/2.21 tff(9551,plain,
% 2.03/2.21 (b(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9550, 6668])).
% 2.03/2.21 tff(9552,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[4186, 9113])).
% 2.03/2.21 tff(9553,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9554,plain,
% 2.03/2.21 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(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(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9555,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(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(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9554])).
% 2.03/2.21 tff(9556,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(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(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9555, 9553])).
% 2.03/2.21 tff(9557,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(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(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9558,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9557, 9556])).
% 2.03/2.22 tff(9559,plain,
% 2.03/2.22 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9558, 245, 9552, 9551, 9548, 9547])).
% 2.03/2.22 tff(9560,plain,
% 2.03/2.22 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9559, 9545])).
% 2.03/2.22 tff(9561,plain,
% 2.03/2.22 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[353, 9560, 11])).
% 2.03/2.22 tff(9562,plain,
% 2.03/2.22 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[415, 9561, 406])).
% 2.03/2.22 tff(9563,plain,
% 2.03/2.22 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1239, 9562, 1309])).
% 2.03/2.22 tff(9564,plain,
% 2.03/2.22 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9563, 9544])).
% 2.03/2.22 tff(9565,plain,
% 2.03/2.22 (~b(z, s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4562, 9564, 234, 4186])).
% 2.03/2.22 tff(9566,plain,
% 2.03/2.22 (~b(z, elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4808, 3523, 422])).
% 2.03/2.22 tff(9567,plain,
% 2.03/2.22 (r(z, elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[175, 9566, 118])).
% 2.03/2.22 tff(9568,plain,
% 2.03/2.22 (~b(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8656, 9550, 422, 556, 9552, 164, 9])).
% 2.03/2.22 tff(9569,plain,
% 2.03/2.22 (b(s(z), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9465, 9568, 9567, 4186])).
% 2.03/2.22 tff(9570,plain,
% 2.03/2.22 (~r(z, s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6573, 9564, 4186, 9569, 1717, 9567])).
% 2.03/2.22 tff(9571,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[197, 9570, 9565])).
% 2.03/2.22 tff(9572,plain,(b(z, s(s(s(s(elem!1))))) | (~b(elem!1, z)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(9573,plain,
% 2.03/2.22 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9572, 9538, 1673, 8920, 9488, 1304, 9476, 11, 9542, 7, 9])).
% 2.03/2.22 tff(9574,plain,
% 2.03/2.22 (b(z, elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9573, 9540])).
% 2.03/2.22 tff(9575,plain,
% 2.03/2.22 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8225, 9574, 11, 7316, 9538])).
% 2.03/2.22 tff(9576,plain,
% 2.03/2.22 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[110, 9575, 96])).
% 2.03/2.22 tff(9577,plain,
% 2.03/2.22 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9576, 9497])).
% 2.03/2.22 tff(9578,plain,
% 2.03/2.22 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[415, 9577, 9476])).
% 2.03/2.22 tff(9579,plain,
% 2.03/2.22 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[353, 9578, 11])).
% 2.03/2.22 tff(9580,plain,
% 2.03/2.22 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9505])).
% 2.03/2.22 tff(9581,plain,
% 2.03/2.22 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9580])).
% 2.03/2.22 tff(9582,plain,
% 2.03/2.22 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.22 tff(9583,plain,
% 2.03/2.22 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9538, 9582])).
% 2.03/2.22 tff(9584,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9585,plain,
% 2.03/2.22 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9586,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9585])).
% 2.03/2.22 tff(9587,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9586, 9584])).
% 2.03/2.22 tff(9588,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9589,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9588, 9587])).
% 2.03/2.22 tff(9590,plain,
% 2.03/2.22 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9589, 245, 9573, 9583, 9517])).
% 2.03/2.22 tff(9591,plain,
% 2.03/2.22 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9590, 9581])).
% 2.03/2.22 tff(9592,plain,
% 2.03/2.22 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1320, 9591, 1312])).
% 2.03/2.22 tff(9593,plain,
% 2.03/2.22 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9501])).
% 2.03/2.22 tff(9594,plain,
% 2.03/2.22 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9542, 9593])).
% 2.03/2.22 tff(9595,plain,
% 2.03/2.22 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(z))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[1153, 9243])).
% 2.03/2.22 tff(9596,plain,
% 2.03/2.22 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9238, 245, 2197, 1943, 1596])).
% 2.03/2.22 tff(9597,plain,
% 2.03/2.22 (r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6665, 32, 463, 9596])).
% 2.03/2.22 tff(9598,plain,
% 2.03/2.22 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9250, 141, 9597, 722])).
% 2.03/2.22 tff(9599,plain,
% 2.03/2.22 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9254, 32, 9598])).
% 2.03/2.22 tff(9600,plain,
% 2.03/2.22 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9599, 9595])).
% 2.03/2.22 tff(9601,plain,
% 2.03/2.22 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.22 inference(symmetry,[status(thm)],[9099])).
% 2.03/2.22 tff(9602,plain,
% 2.03/2.22 ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9601])).
% 2.03/2.22 tff(9603,plain,
% 2.03/2.22 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[6651])).
% 2.03/2.22 tff(9604,plain,
% 2.03/2.22 (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(s(elem!1))))))))),
% 2.03/2.22 inference(symmetry,[status(thm)],[9603])).
% 2.03/2.22 tff(9605,plain,
% 2.03/2.22 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[2751, 9604])).
% 2.03/2.22 tff(9606,plain,
% 2.03/2.22 (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9377, 141, 9597, 722])).
% 2.03/2.22 tff(9607,plain,
% 2.03/2.22 ((s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9165, 32, 9606])).
% 2.03/2.22 tff(9608,plain,
% 2.03/2.22 (b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9607, 9326])).
% 2.03/2.22 tff(9609,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9610,plain,
% 2.03/2.22 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9611,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9610])).
% 2.03/2.22 tff(9612,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9611, 9609])).
% 2.03/2.22 tff(9613,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9614,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9613, 9612])).
% 2.03/2.22 tff(9615,plain,
% 2.03/2.22 ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9614, 245, 9600, 9608])).
% 2.03/2.22 tff(9616,plain,
% 2.03/2.22 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9615, 6654])).
% 2.03/2.22 tff(9617,plain,
% 2.03/2.22 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[797, 9616, 9097])).
% 2.03/2.22 tff(9618,plain,
% 2.03/2.22 (((~![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(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(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)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9619,plain,
% 2.03/2.22 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9620,plain,
% 2.03/2.22 (((~![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(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(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)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9619])).
% 2.03/2.22 tff(9621,plain,
% 2.03/2.22 (((~![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(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(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)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9620, 9618])).
% 2.03/2.22 tff(9622,plain,
% 2.03/2.22 ((~![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(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9623,plain,
% 2.03/2.22 ((~![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(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9622, 9621])).
% 2.03/2.22 tff(9624,plain,
% 2.03/2.22 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9623, 141, 9617])).
% 2.03/2.22 tff(9625,plain,
% 2.03/2.22 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9624, 9605])).
% 2.03/2.22 tff(9626,plain,
% 2.03/2.22 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9625, 9602])).
% 2.03/2.22 tff(9627,plain,
% 2.03/2.22 (b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[787, 9626, 9101])).
% 2.03/2.22 tff(9628,plain,
% 2.03/2.22 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9627, 9102])).
% 2.03/2.22 tff(9629,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9630,plain,
% 2.03/2.22 (((~b(z, 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(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9631,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9630])).
% 2.03/2.22 tff(9632,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9631, 9629])).
% 2.03/2.22 tff(9633,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(s(z))))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9634,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9633, 9632])).
% 2.03/2.22 tff(9635,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9634, 245, 2197, 1943, 1596, 9628, 9600])).
% 2.03/2.22 tff(9636,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(9637,plain,
% 2.03/2.22 (~r(s(s(s(s(s(z))))), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9636, 9573, 9583, 9594, 9488, 9592, 9579, 9496])).
% 2.03/2.22 tff(9638,plain,
% 2.03/2.22 (b(s(s(s(s(s(z))))), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[738, 9637])).
% 2.03/2.22 tff(9639,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9640,plain,
% 2.03/2.22 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9641,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9640])).
% 2.03/2.22 tff(9642,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9641, 9639])).
% 2.03/2.22 tff(9643,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9644,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9643, 9642])).
% 2.03/2.22 tff(9645,plain,
% 2.03/2.22 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9644, 245, 9573, 9583, 9638])).
% 2.03/2.22 tff(9646,plain,
% 2.03/2.22 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9645, 9495])).
% 2.03/2.22 tff(9647,plain,
% 2.03/2.22 (r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[787, 9646, 9492])).
% 2.03/2.22 tff(9648,plain,
% 2.03/2.22 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9647, 9489])).
% 2.03/2.22 tff(9649,plain,
% 2.03/2.22 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6872, 9490])).
% 2.03/2.22 tff(9650,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9651,plain,
% 2.03/2.22 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9652,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9651])).
% 2.03/2.22 tff(9653,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9652, 9650])).
% 2.03/2.22 tff(9654,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9655,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9654, 9653])).
% 2.03/2.23 tff(9656,plain,
% 2.03/2.23 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9655, 245, 9573, 9583, 9638, 9517])).
% 2.03/2.23 tff(9657,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[797, 9656, 9649])).
% 2.03/2.23 tff(9658,plain,
% 2.03/2.23 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9505])).
% 2.03/2.23 tff(9659,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9658])).
% 2.03/2.23 tff(9660,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9497, 9659])).
% 2.03/2.23 tff(9661,plain,
% 2.03/2.23 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9576, 9660])).
% 2.03/2.23 tff(9662,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9219, 141, 9661, 9657, 9648])).
% 2.03/2.23 tff(9663,plain,((s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9664,plain,
% 2.03/2.23 (s(s(s(elem!1))) = s(elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9663, 9, 1, 8])).
% 2.03/2.23 tff(9665,plain,
% 2.03/2.23 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8912, 9664, 9476])).
% 2.03/2.23 tff(9666,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9488])).
% 2.03/2.23 tff(9667,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(symmetry,[status(thm)],[9666])).
% 2.03/2.23 tff(9668,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[559, 9664, 9542])).
% 2.03/2.23 tff(9669,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9668, 9667])).
% 2.03/2.23 tff(9670,plain,
% 2.03/2.23 (s(s(s(s(elem!1)))) = elem!1),
% 2.03/2.23 inference(symmetry,[status(thm)],[9488])).
% 2.03/2.23 tff(9671,plain,
% 2.03/2.23 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), elem!1)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9670])).
% 2.03/2.23 tff(9672,plain,
% 2.03/2.23 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9671])).
% 2.03/2.23 tff(9673,plain,
% 2.03/2.23 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9670])).
% 2.03/2.23 tff(9674,plain,
% 2.03/2.23 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = elem!1)),
% 2.03/2.23 inference(transitivity,[status(thm)],[9673, 339])).
% 2.03/2.23 tff(9675,plain,
% 2.03/2.23 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9674])).
% 2.03/2.23 tff(9676,plain,
% 2.03/2.23 (~(s(z) = elem!1)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[209, 9675])).
% 2.03/2.23 tff(9677,plain,
% 2.03/2.23 (~r(z, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3608, 9007, 9665])).
% 2.03/2.23 tff(9678,plain,
% 2.03/2.23 (b(z, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[197, 9677])).
% 2.03/2.23 tff(9679,plain,
% 2.03/2.23 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9673])).
% 2.03/2.23 tff(9680,plain,
% 2.03/2.23 (~(elem!1 = s(z))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[209, 9679])).
% 2.03/2.23 tff(9681,plain,
% 2.03/2.23 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1949, 89, 9490])).
% 2.03/2.23 tff(9682,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2558, 9681])).
% 2.03/2.23 tff(9683,plain,
% 2.03/2.23 (~r(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5649, 9682, 7316, 348, 9476, 9007, 9490])).
% 2.03/2.23 tff(9684,plain,
% 2.03/2.23 (b(elem!1, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[281, 9683, 9680])).
% 2.03/2.23 tff(9685,plain,
% 2.03/2.23 (~b(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[6764, 9684, 9669, 9678, 9016])).
% 2.03/2.23 tff(9686,plain,
% 2.03/2.23 (r(s(z), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[389, 9685, 9676])).
% 2.03/2.23 tff(9687,plain,
% 2.03/2.23 (r(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9686, 9672])).
% 2.03/2.23 tff(9688,plain,
% 2.03/2.23 (~b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5746, 9686, 9476, 9007, 9, 9490, 9682])).
% 2.03/2.23 tff(9689,plain,
% 2.03/2.23 (r(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[232, 9688])).
% 2.03/2.23 tff(9690,plain,
% 2.03/2.23 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3376, 141, 9689, 9682])).
% 2.03/2.23 tff(9691,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9690, 9687])).
% 2.03/2.23 tff(9692,plain,(b(elem!1, z) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9693,plain,
% 2.03/2.23 (b(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9692, 9, 1, 8])).
% 2.03/2.23 tff(9694,plain,
% 2.03/2.23 (~b(z, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4562, 9693, 8920, 9669])).
% 2.03/2.23 tff(9695,plain,
% 2.03/2.23 (r(z, s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[197, 9694])).
% 2.03/2.23 tff(9696,plain,
% 2.03/2.23 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9503])).
% 2.03/2.23 tff(9697,plain,
% 2.03/2.23 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9696])).
% 2.03/2.23 tff(9698,plain,
% 2.03/2.23 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9697])).
% 2.03/2.23 tff(9699,plain,
% 2.03/2.23 (s(elem!1) = s(s(s(elem!1)))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9664])).
% 2.03/2.23 tff(9700,plain,
% 2.03/2.23 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9699, 9698])).
% 2.03/2.23 tff(9701,plain,
% 2.03/2.23 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9700])).
% 2.03/2.23 tff(9702,plain,
% 2.03/2.23 (b(s(s(s(s(s(s(s(elem!1))))))), z) <=> b(s(elem!1), z)),
% 2.03/2.23 inference(symmetry,[status(thm)],[9701])).
% 2.03/2.23 tff(9703,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9698])).
% 2.03/2.23 tff(9704,plain,
% 2.03/2.23 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[8920, 9703])).
% 2.03/2.23 tff(9705,plain,
% 2.03/2.23 (b(s(elem!1), z)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9704, 9702])).
% 2.03/2.23 tff(9706,plain,
% 2.03/2.23 (~b(z, elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[7707, 9693, 7316, 9705])).
% 2.03/2.23 tff(9707,plain,
% 2.03/2.23 (r(z, elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[175, 9706, 118])).
% 2.03/2.23 tff(9708,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2078, 9707, 9695, 9665])).
% 2.03/2.23 tff(9709,plain,((s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9710,plain,
% 2.03/2.23 (s(z) = s(elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9709, 8, 1])).
% 2.03/2.23 tff(9711,plain,
% 2.03/2.23 (z = elem!1),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[57, 9710])).
% 2.03/2.23 tff(9712,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9711])).
% 2.03/2.23 tff(9713,plain,
% 2.03/2.23 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1968, 9711, 8])).
% 2.03/2.23 tff(9714,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2558, 9713])).
% 2.03/2.23 tff(9715,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9714, 9712])).
% 2.03/2.23 tff(9716,plain,
% 2.03/2.23 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9710])).
% 2.03/2.23 tff(9717,plain,
% 2.03/2.23 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9716, 1939])).
% 2.03/2.23 tff(9718,plain,
% 2.03/2.23 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9717])).
% 2.03/2.23 tff(9719,plain,
% 2.03/2.23 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[1128, 9718])).
% 2.03/2.23 tff(9720,plain,
% 2.03/2.23 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9711])).
% 2.03/2.23 tff(9721,plain,
% 2.03/2.23 (b(s(z), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[7687, 9711, 7316])).
% 2.03/2.23 tff(9722,plain,
% 2.03/2.23 (elem!1 = z),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3643, 9711])).
% 2.03/2.23 tff(9723,plain,
% 2.03/2.23 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9711])).
% 2.03/2.23 tff(9724,plain,
% 2.03/2.23 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9723, 61])).
% 2.03/2.23 tff(9725,plain,
% 2.03/2.23 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9724])).
% 2.03/2.23 tff(9726,plain,
% 2.03/2.23 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[66, 9725])).
% 2.03/2.23 tff(9727,plain,
% 2.03/2.23 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.03/2.23 inference(symmetry,[status(thm)],[7411])).
% 2.03/2.23 tff(9728,plain,
% 2.03/2.23 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[7414, 9727])).
% 2.03/2.23 tff(9729,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9728])).
% 2.03/2.23 tff(9730,plain,
% 2.03/2.23 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[7414, 9727])).
% 2.03/2.23 tff(9731,plain,
% 2.03/2.23 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9730])).
% 2.03/2.23 tff(9732,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[7413])).
% 2.03/2.23 tff(9733,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[120])).
% 2.03/2.23 tff(9734,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.23 inference(transitivity,[status(thm)],[9733, 9732])).
% 2.03/2.23 tff(9735,plain,
% 2.03/2.23 ((elem!1 = s(s(s(s(s(z)))))) <=> (z = s(s(s(s(s(z))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[120])).
% 2.03/2.23 tff(9736,plain,
% 2.03/2.23 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.03/2.23 inference(transitivity,[status(thm)],[9735, 750])).
% 2.03/2.23 tff(9737,plain,
% 2.03/2.23 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9736])).
% 2.03/2.23 tff(9738,plain,
% 2.03/2.23 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.03/2.23 inference(transitivity,[status(thm)],[9737, 1470])).
% 2.03/2.23 tff(9739,plain,
% 2.03/2.23 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9738])).
% 2.03/2.23 tff(9740,plain,
% 2.03/2.23 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[734, 9739])).
% 2.03/2.23 tff(9741,plain,
% 2.03/2.23 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[120])).
% 2.03/2.23 tff(9742,plain,
% 2.03/2.23 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9741])).
% 2.03/2.23 tff(9743,plain,
% 2.03/2.23 (b(z, s(z)) <=> b(z, s(elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[3890])).
% 2.03/2.23 tff(9744,plain,
% 2.03/2.23 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9743, 9742])).
% 2.03/2.23 tff(9745,plain,
% 2.03/2.23 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[120])).
% 2.03/2.23 tff(9746,plain,
% 2.03/2.23 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9745])).
% 2.03/2.23 tff(9747,plain,
% 2.03/2.23 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[2069, 9746])).
% 2.03/2.23 tff(9748,plain,
% 2.03/2.23 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4226, 1449, 106])).
% 2.03/2.23 tff(9749,plain,
% 2.03/2.23 (r(s(z), s(elem!1)) <=> r(s(elem!1), s(elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[3890])).
% 2.03/2.23 tff(9750,plain,
% 2.03/2.23 (r(s(elem!1), s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9749])).
% 2.03/2.23 tff(9751,plain,
% 2.03/2.23 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(z), s(elem!1)))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9750])).
% 2.03/2.23 tff(9752,plain,
% 2.03/2.23 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 2.03/2.23 inference(bind,[status(th)],[])).
% 2.03/2.23 tff(9753,plain,
% 2.03/2.23 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.03/2.23 inference(quant_intro,[status(thm)],[9752])).
% 2.03/2.23 tff(9754,plain,
% 2.03/2.23 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9755,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 2.03/2.23 tff(9756,plain,
% 2.03/2.23 (![X: $i] : (~r(X, X))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9755, 9754])).
% 2.03/2.23 tff(9757,plain,(
% 2.03/2.23 ![X: $i] : (~r(X, X))),
% 2.03/2.23 inference(skolemize,[status(sab)],[9756])).
% 2.03/2.23 tff(9758,plain,
% 2.03/2.23 (![X: $i] : (~r(X, X))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9757, 9753])).
% 2.03/2.23 tff(9759,plain,
% 2.03/2.23 ((~![X: $i] : (~r(X, X))) | (~r(s(elem!1), s(elem!1)))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9760,plain,
% 2.03/2.23 (~r(s(elem!1), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9759, 9758])).
% 2.03/2.23 tff(9761,plain,
% 2.03/2.23 (~r(s(z), s(elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9760, 9751])).
% 2.03/2.23 tff(9762,plain,
% 2.03/2.23 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[120])).
% 2.03/2.23 tff(9763,plain,
% 2.03/2.23 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9762])).
% 2.03/2.23 tff(9764,plain,
% 2.03/2.23 (r(z, s(z)) <=> r(z, s(elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[3890])).
% 2.03/2.23 tff(9765,plain,
% 2.03/2.23 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9764, 9763])).
% 2.03/2.23 tff(9766,plain,
% 2.03/2.23 (r(elem!1, s(elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[1449, 9765])).
% 2.03/2.23 tff(9767,plain,
% 2.03/2.23 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1384, 9766, 130])).
% 2.03/2.23 tff(9768,plain,
% 2.03/2.23 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[420, 9767, 7])).
% 2.03/2.23 tff(9769,plain,
% 2.03/2.23 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2772, 9768, 130, 2338, 1312, 2070, 9766])).
% 2.03/2.23 tff(9770,plain,
% 2.03/2.23 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1263, 1259, 1])).
% 2.03/2.23 tff(9771,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[39])).
% 2.03/2.23 tff(9772,plain,
% 2.03/2.23 ((~r(s(s(s(s(elem!1)))), s(z))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9771])).
% 2.03/2.23 tff(9773,plain,
% 2.03/2.23 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[212, 9772])).
% 2.03/2.23 tff(9774,plain,
% 2.03/2.23 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[420, 9773, 7])).
% 2.03/2.23 tff(9775,plain,
% 2.03/2.23 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[58])).
% 2.03/2.23 tff(9776,plain,
% 2.03/2.23 (~r(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4959, 1366, 106])).
% 2.03/2.23 tff(9777,plain,
% 2.03/2.23 (b(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[653, 32, 638, 9776])).
% 2.03/2.23 tff(9778,plain,
% 2.03/2.23 (b(s(elem!1), elem!1)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9777, 9775])).
% 2.03/2.23 tff(9779,plain,
% 2.03/2.23 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[2197, 3517])).
% 2.03/2.23 tff(9780,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1461, 39, 9779, 9778, 9774, 96, 1366, 1379, 399])).
% 2.03/2.23 tff(9781,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1257, 9780, 1379, 1])).
% 2.03/2.23 tff(9782,plain,
% 2.03/2.23 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1252, 1561])).
% 2.03/2.23 tff(9783,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1239, 9780, 9782])).
% 2.03/2.23 tff(9784,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2377, 9783, 1366])).
% 2.03/2.23 tff(9785,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[353, 9784, 1561])).
% 2.03/2.23 tff(9786,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9028, 245, 9785, 9779, 9778, 9781, 9774])).
% 2.03/2.23 tff(9787,plain,((~(s(z) = s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9788,plain,
% 2.03/2.23 (~(s(z) = s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9787, 9770, 1, 399, 106, 2197, 212])).
% 2.03/2.23 tff(9789,plain,
% 2.03/2.23 (~(z = elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[117, 9788])).
% 2.03/2.23 tff(9790,plain,
% 2.03/2.23 (~(elem!1 = z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[123, 9789])).
% 2.03/2.23 tff(9791,plain,
% 2.03/2.23 (~r(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4959, 9770, 106])).
% 2.03/2.23 tff(9792,plain,
% 2.03/2.23 (b(s(elem!1), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[653, 32, 638, 9791])).
% 2.03/2.23 tff(9793,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 2.03/2.23 tff(9794,plain,
% 2.03/2.23 (b(s(z), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[440, 9788, 9793])).
% 2.03/2.23 tff(9795,plain,
% 2.03/2.23 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1274, 564, 1, 1259])).
% 2.03/2.23 tff(9796,plain,
% 2.03/2.23 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[151, 9795, 7790])).
% 2.03/2.23 tff(9797,plain,
% 2.03/2.23 (r(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[568, 32, 564, 105])).
% 2.03/2.23 tff(9798,plain,
% 2.03/2.23 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2837, 9797, 9770])).
% 2.03/2.23 tff(9799,plain,
% 2.03/2.23 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1432, 9798, 399])).
% 2.03/2.23 tff(9800,plain,
% 2.03/2.23 (~r(z, elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[663, 9797, 655, 355])).
% 2.03/2.23 tff(9801,plain,
% 2.03/2.23 (b(z, elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[175, 9800, 55])).
% 2.03/2.23 tff(9802,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5132, 245, 9801, 9799, 2197, 9796])).
% 2.03/2.23 tff(9803,plain,(b(s(elem!1), elem!1) | (~b(z, s(s(s(s(elem!1)))))) | (z = elem!1) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9804,plain,
% 2.03/2.23 (b(s(elem!1), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9803, 9789, 2197, 399, 9794, 355, 1, 1259])).
% 2.03/2.23 tff(9805,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9806,plain,
% 2.03/2.23 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9807,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9806])).
% 2.03/2.23 tff(9808,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9807, 9805])).
% 2.03/2.23 tff(9809,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9810,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9809, 9808])).
% 2.03/2.23 tff(9811,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9810, 245, 4186, 308, 288, 2197, 2824])).
% 2.03/2.23 tff(9812,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9813,plain,
% 2.03/2.23 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9812, 4186, 308, 288, 2197])).
% 2.03/2.23 tff(9814,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[151, 9813, 2562])).
% 2.03/2.23 tff(9815,plain,
% 2.03/2.23 (~b(z, elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[7707, 4186, 308, 288])).
% 2.03/2.23 tff(9816,plain,
% 2.03/2.23 (r(z, elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[175, 9815, 55])).
% 2.03/2.23 tff(9817,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2589, 141, 9816, 9814, 106])).
% 2.03/2.23 tff(9818,plain,((~b(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (z = elem!1) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9819,plain,
% 2.03/2.23 (~b(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9818, 9789, 106, 9804, 9792, 7790, 2197])).
% 2.03/2.23 tff(9820,plain,
% 2.03/2.23 (r(elem!1, z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[128, 9819, 9790])).
% 2.03/2.23 tff(9821,plain,
% 2.03/2.23 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[144, 141, 9820, 106])).
% 2.03/2.23 tff(9822,plain,
% 2.03/2.23 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[151, 9821, 7790])).
% 2.03/2.23 tff(9823,plain,
% 2.03/2.23 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5214, 9820, 106])).
% 2.03/2.23 tff(9824,plain,
% 2.03/2.23 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1432, 9823, 399])).
% 2.03/2.23 tff(9825,plain,
% 2.03/2.23 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[7347, 245, 9824, 9804, 9822])).
% 2.03/2.23 tff(9826,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[420, 9825, 7])).
% 2.03/2.23 tff(9827,plain,
% 2.03/2.23 (~r(z, s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1350, 9826, 106])).
% 2.03/2.23 tff(9828,plain,
% 2.03/2.23 (b(z, s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[644, 9827])).
% 2.03/2.23 tff(9829,plain,
% 2.03/2.23 (((~b(z, s(elem!1))) | (~b(s(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), s(elem!1))) | (~b(s(z), z)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9830,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(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(X0, 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), s(elem!1))) | (~b(s(z), z))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9829])).
% 2.03/2.23 tff(9831,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(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(X0, 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), s(elem!1))) | (~b(s(z), z)))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9830, 656])).
% 2.03/2.23 tff(9832,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9833,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), z))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9832, 9831])).
% 2.03/2.23 tff(9834,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9833, 245, 355, 9794, 9792, 9828])).
% 2.03/2.23 tff(9835,plain,(b(s(elem!1), s(s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (elem!1 = s(s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(elem!1))))) | r(s(z), s(elem!1)) | r(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9836,plain,
% 2.03/2.23 (~b(z, s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9835, 9769, 399, 9761, 355, 1, 106, 9748])).
% 2.03/2.23 tff(9837,plain,
% 2.03/2.23 (r(z, s(elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[1449, 9764])).
% 2.03/2.23 tff(9838,plain,
% 2.03/2.23 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1263, 9769, 1])).
% 2.03/2.23 tff(9839,plain,
% 2.03/2.23 (~r(z, s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5050, 9838, 9837])).
% 2.03/2.23 tff(9840,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1992, 9839, 9836])).
% 2.03/2.23 tff(9841,plain,((~r(z, s(z))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(z), z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9842,plain,
% 2.03/2.23 (~r(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9841, 9747, 355, 1, 106, 130, 399, 120])).
% 2.03/2.23 tff(9843,plain,
% 2.03/2.23 (b(z, s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1421, 9842])).
% 2.03/2.23 tff(9844,plain,
% 2.03/2.23 (b(elem!1, s(elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9843, 9744])).
% 2.03/2.23 tff(9845,plain,
% 2.03/2.23 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2756, 9747, 130])).
% 2.03/2.23 tff(9846,plain,
% 2.03/2.23 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1320, 9845, 1312])).
% 2.03/2.23 tff(9847,plain,
% 2.03/2.23 (b(z, s(elem!1))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9843, 9743])).
% 2.03/2.23 tff(9848,plain,
% 2.03/2.23 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[120])).
% 2.03/2.23 tff(9849,plain,
% 2.03/2.23 (b(s(elem!1), z)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[7316, 9848])).
% 2.03/2.23 tff(9850,plain,
% 2.03/2.23 (((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9851,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9850])).
% 2.03/2.23 tff(9852,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9851, 2866])).
% 2.03/2.23 tff(9853,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9854,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9853, 9852])).
% 2.03/2.23 tff(9855,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9854, 245, 234, 9849, 9847])).
% 2.03/2.23 tff(9856,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[353, 9855, 2338])).
% 2.03/2.23 tff(9857,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2395, 9856, 399, 9844, 9747, 1])).
% 2.03/2.23 tff(9858,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1239, 9857, 1304])).
% 2.03/2.23 tff(9859,plain,
% 2.03/2.23 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1919, 9858, 2692, 7316, 9846, 3890, 9844, 1])).
% 2.03/2.23 tff(9860,plain,
% 2.03/2.23 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[7422, 9859, 120])).
% 2.03/2.23 tff(9861,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[787, 9860, 9740])).
% 2.03/2.23 tff(9862,plain,
% 2.03/2.23 (r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9861, 9734])).
% 2.03/2.23 tff(9863,plain,
% 2.03/2.23 (((~![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(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9864,plain,
% 2.03/2.23 ((~![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(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9865,plain,
% 2.03/2.23 ((~![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(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9864, 9863])).
% 2.03/2.23 tff(9866,plain,
% 2.03/2.23 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9865, 141, 106, 9862])).
% 2.03/2.23 tff(9867,plain,
% 2.03/2.23 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1526, 32, 1490, 9866])).
% 2.03/2.23 tff(9868,plain,
% 2.03/2.23 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1664, 245, 9846, 9858, 9867])).
% 2.03/2.23 tff(9869,plain,
% 2.03/2.23 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9868, 9731])).
% 2.03/2.23 tff(9870,plain,
% 2.03/2.23 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[909, 9869])).
% 2.03/2.23 tff(9871,plain,
% 2.03/2.24 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9870, 9729])).
% 2.03/2.24 tff(9872,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9873,plain,
% 2.03/2.24 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9874,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(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, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9873])).
% 2.03/2.24 tff(9875,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(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, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9874, 9872])).
% 2.03/2.24 tff(9876,plain,
% 2.03/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9877,plain,
% 2.03/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9876, 9875])).
% 2.03/2.24 tff(9878,plain,
% 2.03/2.24 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9877, 141, 2069, 9862])).
% 2.03/2.24 tff(9879,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9878, 9871])).
% 2.03/2.24 tff(9880,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~(elem!1 = z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(9881,plain,
% 2.03/2.24 (~r(z, s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9880, 9726, 8920, 1, 9722, 9714, 9721, 9715])).
% 2.03/2.24 tff(9882,plain,
% 2.03/2.24 (b(z, s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[197, 9881])).
% 2.03/2.24 tff(9883,plain,
% 2.03/2.24 (b(elem!1, s(s(s(elem!1))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9882, 9720])).
% 2.03/2.24 tff(9884,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9711])).
% 2.03/2.24 tff(9885,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8920, 9884])).
% 2.03/2.24 tff(9886,plain,
% 2.03/2.24 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8712, 245, 7316, 9885, 9883])).
% 2.03/2.24 tff(9887,plain,
% 2.03/2.24 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[353, 9886, 9719])).
% 2.03/2.24 tff(9888,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1571, 9710, 1])).
% 2.03/2.24 tff(9889,plain,
% 2.03/2.24 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9711])).
% 2.03/2.24 tff(9890,plain,
% 2.03/2.24 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9889, 1547])).
% 2.03/2.24 tff(9891,plain,
% 2.03/2.24 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.03/2.24 inference(transitivity,[status(thm)],[9890, 1548])).
% 2.03/2.24 tff(9892,plain,
% 2.03/2.24 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9891])).
% 2.03/2.24 tff(9893,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[1554, 9892])).
% 2.03/2.24 tff(9894,plain,
% 2.03/2.24 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9711])).
% 2.03/2.24 tff(9895,plain,
% 2.03/2.24 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9894, 770])).
% 2.03/2.24 tff(9896,plain,
% 2.03/2.24 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.03/2.24 inference(transitivity,[status(thm)],[9895, 1470])).
% 2.03/2.24 tff(9897,plain,
% 2.03/2.24 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9896])).
% 2.03/2.24 tff(9898,plain,
% 2.03/2.24 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[734, 9897])).
% 2.03/2.24 tff(9899,plain,
% 2.03/2.24 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[2639])).
% 2.03/2.24 tff(9900,plain,
% 2.03/2.24 (b(s(elem!1), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[1682, 2637, 9899])).
% 2.03/2.24 tff(9901,plain,
% 2.03/2.24 ((~b(s(elem!1), s(s(s(s(s(elem!1))))))) <=> (~b(s(z), s(s(s(s(s(z)))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9900])).
% 2.03/2.24 tff(9902,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9903,plain,
% 2.03/2.24 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9904,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9903])).
% 2.03/2.24 tff(9905,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9904, 9902])).
% 2.03/2.24 tff(9906,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9907,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9906, 9905])).
% 2.03/2.24 tff(9908,plain,
% 2.03/2.24 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9907, 245, 308, 1427, 2101, 1543])).
% 2.03/2.24 tff(9909,plain,
% 2.03/2.24 (~b(s(z), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9908, 9901])).
% 2.03/2.24 tff(9910,plain,
% 2.03/2.24 (r(s(z), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1698, 9909])).
% 2.03/2.24 tff(9911,plain,
% 2.03/2.24 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9910, 7574])).
% 2.03/2.24 tff(9912,plain,
% 2.03/2.24 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 2.03/2.24 inference(commutativity,[status(thm)],[])).
% 2.03/2.24 tff(9913,plain,
% 2.03/2.24 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = s(elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[39])).
% 2.03/2.24 tff(9914,plain,
% 2.03/2.24 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(s(s(z))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9913, 9912])).
% 2.03/2.24 tff(9915,plain,
% 2.03/2.24 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9914])).
% 2.03/2.24 tff(9916,plain,
% 2.03/2.24 (~(s(elem!1) = s(s(s(z))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[892, 9915])).
% 2.03/2.24 tff(9917,plain,
% 2.03/2.24 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[1492])).
% 2.03/2.24 tff(9918,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(symmetry,[status(thm)],[9917])).
% 2.03/2.24 tff(9919,plain,
% 2.03/2.24 (b(s(s(s(z))), elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[1427, 9918])).
% 2.03/2.24 tff(9920,plain,
% 2.03/2.24 (~b(s(elem!1), s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8464, 2101, 1427, 9919, 308])).
% 2.03/2.24 tff(9921,plain,
% 2.03/2.24 (r(s(elem!1), s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8469, 9920, 9916])).
% 2.03/2.24 tff(9922,plain,
% 2.03/2.24 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[2733, 7392])).
% 2.03/2.24 tff(9923,plain,
% 2.03/2.24 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1515, 9922])).
% 2.03/2.24 tff(9924,plain,
% 2.03/2.24 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8472, 9923, 9921])).
% 2.03/2.24 tff(9925,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9924, 9911])).
% 2.03/2.24 tff(9926,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(9927,plain,
% 2.03/2.24 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9926, 9710, 9885, 9883, 7316])).
% 2.03/2.24 tff(9928,plain,
% 2.03/2.24 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[7422, 9927, 9722])).
% 2.03/2.24 tff(9929,plain,
% 2.03/2.24 (r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[787, 9928, 9898])).
% 2.03/2.24 tff(9930,plain,
% 2.03/2.24 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3714, 9929, 9710])).
% 2.03/2.24 tff(9931,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[331, 9719])).
% 2.03/2.24 tff(9932,plain,
% 2.03/2.24 (((~![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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9933,plain,
% 2.03/2.24 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9934,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(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(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9933])).
% 2.03/2.24 tff(9935,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(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(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9934, 9932])).
% 2.03/2.24 tff(9936,plain,
% 2.03/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9937,plain,
% 2.03/2.24 ((~![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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9936, 9935])).
% 2.03/2.24 tff(9938,plain,
% 2.03/2.24 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9937, 141, 9715, 9930])).
% 2.03/2.24 tff(9939,plain,
% 2.03/2.24 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1750, 32, 9938])).
% 2.03/2.24 tff(9940,plain,
% 2.03/2.24 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9939, 1740])).
% 2.03/2.24 tff(9941,plain,
% 2.03/2.24 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1520, 141, 9715, 9930])).
% 2.03/2.24 tff(9942,plain,
% 2.03/2.24 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1526, 32, 1490, 9941])).
% 2.03/2.24 tff(9943,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(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(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9944,plain,
% 2.03/2.24 (((~r(s(s(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(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9945,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9944])).
% 2.03/2.24 tff(9946,plain,
% 2.03/2.24 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9945, 9943])).
% 2.03/2.24 tff(9947,plain,
% 2.03/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(elem!1)))))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9948,plain,
% 2.03/2.24 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9947, 9946])).
% 2.03/2.24 tff(9949,plain,
% 2.03/2.24 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9948, 141, 2700, 1501])).
% 2.03/2.24 tff(9950,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.03/2.24 tff(9951,plain,
% 2.03/2.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9952,plain,
% 2.03/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9953,plain,
% 2.03/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9952, 9951])).
% 2.03/2.24 tff(9954,plain,
% 2.03/2.24 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9953, 32, 9950, 9949])).
% 2.03/2.24 tff(9955,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(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(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(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(s(s(elem!1)))))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9956,plain,
% 2.03/2.24 (((~b(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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(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(s(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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(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(s(s(elem!1)))))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9957,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(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(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(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(s(s(elem!1))))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9956])).
% 2.03/2.24 tff(9958,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(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(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(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(s(s(elem!1)))))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9957, 9955])).
% 2.03/2.24 tff(9959,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(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(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9960,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9959, 9958])).
% 2.03/2.24 tff(9961,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9960, 245, 2705, 1596, 7400, 9954])).
% 2.03/2.24 tff(9962,plain,((~r(s(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)))), s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(9963,plain,
% 2.03/2.24 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9962, 9942, 9940, 2691, 9931, 9930, 9715])).
% 2.03/2.24 tff(9964,plain,
% 2.03/2.24 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1768, 9963, 9893])).
% 2.03/2.24 tff(9965,plain,
% 2.03/2.24 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[7442])).
% 2.03/2.24 tff(9966,plain,
% 2.03/2.24 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9965])).
% 2.03/2.24 tff(9967,plain,
% 2.03/2.24 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2513, 245, 308, 1427, 1103, 2718])).
% 2.03/2.24 tff(9968,plain,
% 2.03/2.24 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9967, 9966])).
% 2.03/2.24 tff(9969,plain,
% 2.03/2.24 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1630, 9968, 1616])).
% 2.03/2.24 tff(9970,plain,
% 2.03/2.24 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4079, 9969, 39])).
% 2.03/2.24 tff(9971,plain,
% 2.03/2.24 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1775, 245, 308, 1103, 2718])).
% 2.03/2.24 tff(9972,plain,
% 2.03/2.24 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9971, 1546])).
% 2.03/2.24 tff(9973,plain,
% 2.03/2.24 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1820, 9972])).
% 2.03/2.24 tff(9974,plain,
% 2.03/2.24 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9973, 1778])).
% 2.03/2.24 tff(9975,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1907, 141, 371, 9974, 9970])).
% 2.03/2.24 tff(9976,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(9977,plain,
% 2.03/2.24 (~b(elem!1, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9976, 9964, 9710, 9888, 7316, 9885, 9887])).
% 2.03/2.24 tff(9978,plain,
% 2.03/2.24 (r(elem!1, s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2777, 9977, 2563])).
% 2.03/2.24 tff(9979,plain,
% 2.03/2.24 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1384, 9978, 9715])).
% 2.03/2.24 tff(9980,plain,
% 2.03/2.24 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[420, 9979, 7])).
% 2.03/2.24 tff(9981,plain,
% 2.03/2.24 (~(s(s(s(s(s(elem!1))))) = s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[3022, 9710])).
% 2.03/2.24 tff(9982,plain,
% 2.03/2.24 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1520, 141, 130, 1501])).
% 2.03/2.24 tff(9983,plain,
% 2.03/2.24 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1526, 32, 1490, 9982])).
% 2.03/2.24 tff(9984,plain,
% 2.03/2.24 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1384, 1367, 130])).
% 2.03/2.24 tff(9985,plain,
% 2.03/2.24 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[420, 9984, 7])).
% 2.03/2.24 tff(9986,plain,
% 2.03/2.24 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1376, 1367, 1368])).
% 2.03/2.24 tff(9987,plain,
% 2.03/2.24 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1263, 9986, 1])).
% 2.03/2.24 tff(9988,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9989,plain,
% 2.03/2.24 (((~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(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(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))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9990,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9989])).
% 2.03/2.24 tff(9991,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[9990, 9988])).
% 2.03/2.25 tff(9992,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9993,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9992, 9991])).
% 2.03/2.25 tff(9994,plain,
% 2.03/2.25 (~b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9993, 245, 9987, 9985, 9983])).
% 2.03/2.25 tff(9995,plain,
% 2.03/2.25 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3059, 9994, 3053])).
% 2.03/2.25 tff(9996,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3223, 141, 1367, 1501, 9995])).
% 2.03/2.25 tff(9997,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(elem!1))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(9998,plain,
% 2.03/2.25 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9997, 9978, 9981, 1, 9930, 9715])).
% 2.03/2.25 tff(9999,plain,
% 2.03/2.25 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1432, 9998, 9726])).
% 2.03/2.25 tff(10000,plain,
% 2.03/2.25 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1441, 9999, 7316, 9885, 9980])).
% 2.03/2.25 tff(10001,plain,
% 2.03/2.25 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1239, 10000, 1304])).
% 2.03/2.25 tff(10002,plain,
% 2.03/2.25 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2377, 10001, 9887])).
% 2.03/2.25 tff(10003,plain,
% 2.03/2.25 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1263, 10002, 1])).
% 2.03/2.25 tff(10004,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10005,plain,
% 2.03/2.25 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10006,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[10005])).
% 2.03/2.25 tff(10007,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[10006, 10004])).
% 2.03/2.25 tff(10008,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(10009,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[10008, 10007])).
% 2.03/2.25 tff(10010,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10009, 245, 9999, 7316, 10003, 9980])).
% 2.03/2.25 tff(10011,plain,(b(s(s(s(s(elem!1)))), elem!1) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(10012,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10011, 1])).
% 2.03/2.25 tff(10013,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), elem!1) <=> b(elem!1, elem!1)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[6408])).
% 2.03/2.25 tff(10014,plain,
% 2.03/2.25 (b(elem!1, elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.25 inference(symmetry,[status(thm)],[10013])).
% 2.03/2.25 tff(10015,plain,
% 2.03/2.25 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[10014])).
% 2.03/2.25 tff(10016,plain,
% 2.03/2.25 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[79, 10015])).
% 2.03/2.25 tff(10017,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2824, 10016])).
% 2.03/2.25 tff(10018,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(10019,plain,
% 2.03/2.25 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10018, 10012])).
% 2.03/2.25 tff(10020,plain,
% 2.03/2.25 (b(s(elem!1), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1039, 8946])).
% 2.03/2.25 tff(10021,plain,
% 2.03/2.25 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9854, 245, 234, 10020, 8945])).
% 2.03/2.25 tff(10022,plain,
% 2.03/2.25 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[353, 10021, 2338])).
% 2.03/2.25 tff(10023,plain,
% 2.03/2.25 (~r(elem!1, s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2762, 10022, 1367])).
% 2.03/2.25 tff(10024,plain,
% 2.03/2.25 (b(elem!1, s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1724, 10023, 1717])).
% 2.03/2.25 tff(10025,plain,
% 2.03/2.25 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[7371, 10024, 2824, 10022, 1309])).
% 2.03/2.25 tff(10026,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[420, 10025, 164])).
% 2.03/2.25 tff(10027,plain,
% 2.03/2.25 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[7349, 10026, 2824, 308])).
% 2.03/2.25 tff(10028,plain,
% 2.03/2.25 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1432, 10027, 399])).
% 2.03/2.25 tff(10029,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10030,plain,
% 2.03/2.25 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10031,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[10030])).
% 2.03/2.25 tff(10032,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[10031, 10029])).
% 2.03/2.25 tff(10033,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(10034,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[10033, 10032])).
% 2.03/2.25 tff(10035,plain,
% 2.03/2.25 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10034, 245, 308, 10020, 8945, 2824])).
% 2.03/2.25 tff(10036,plain,
% 2.03/2.25 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10035, 10026])).
% 2.03/2.25 tff(10037,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2558, 10036])).
% 2.03/2.25 tff(10038,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[5214, 10037, 10028, 131])).
% 2.03/2.25 tff(10039,plain,((~r(elem!1, z)) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(10040,plain,
% 2.03/2.25 (~r(elem!1, z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10039, 1367, 7316, 10012, 7, 1304, 1673, 399, 8920])).
% 2.03/2.25 tff(10041,plain,
% 2.03/2.25 (b(elem!1, z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[128, 10040, 124])).
% 2.03/2.25 tff(10042,plain,
% 2.03/2.25 (~b(z, elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8118, 10041, 7316, 7790, 1, 9, 2338])).
% 2.03/2.25 tff(10043,plain,
% 2.03/2.25 (r(z, elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[175, 10042, 118])).
% 2.03/2.25 tff(10044,plain,
% 2.03/2.25 (~r(z, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8291, 10043, 1367])).
% 2.03/2.25 tff(10045,plain,
% 2.03/2.25 (b(z, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[644, 10044])).
% 2.03/2.25 tff(10046,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(elem!1, z)) | (~b(z, 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(X0, 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))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10047,plain,
% 2.03/2.25 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10048,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[10047])).
% 2.03/2.25 tff(10049,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[10048, 10046])).
% 2.03/2.25 tff(10050,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(10051,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[10050, 10049])).
% 2.03/2.25 tff(10052,plain,
% 2.03/2.25 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10051, 245, 10041, 7316, 8920, 10045])).
% 2.03/2.25 tff(10053,plain,
% 2.03/2.25 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[353, 10052, 2338])).
% 2.03/2.25 tff(10054,plain,
% 2.03/2.25 (~r(elem!1, s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2762, 10053, 1367])).
% 2.03/2.25 tff(10055,plain,
% 2.03/2.25 (b(elem!1, s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1724, 10054, 1673])).
% 2.03/2.25 tff(10056,plain,
% 2.03/2.25 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[7371, 10055, 10012, 10053, 1304])).
% 2.03/2.25 tff(10057,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10058,plain,
% 2.03/2.25 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10059,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[10058])).
% 2.03/2.25 tff(10060,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[10059, 10057])).
% 2.03/2.25 tff(10061,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(10062,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[10061, 10060])).
% 2.03/2.25 tff(10063,plain,
% 2.03/2.25 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10062, 245, 10041, 7316, 10045, 10012])).
% 2.03/2.25 tff(10064,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2558, 10063])).
% 2.03/2.25 tff(10065,plain,
% 2.03/2.25 (~b(s(elem!1), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8244, 245, 10041, 7316, 10045])).
% 2.03/2.25 tff(10066,plain,
% 2.03/2.25 (r(s(elem!1), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1039, 10065])).
% 2.03/2.25 tff(10067,plain,
% 2.03/2.25 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[4959, 10066, 10064])).
% 2.03/2.25 tff(10068,plain,
% 2.03/2.25 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1263, 10067, 1])).
% 2.03/2.25 tff(10069,plain,
% 2.03/2.25 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[7667, 7791, 308, 556])).
% 2.03/2.25 tff(10070,plain,
% 2.03/2.25 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1432, 10069, 399])).
% 2.03/2.25 tff(10071,plain,
% 2.03/2.25 (~r(z, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3688, 10070, 289])).
% 2.03/2.25 tff(10072,plain,
% 2.03/2.25 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1992, 10071])).
% 2.03/2.25 tff(10073,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10074,plain,
% 2.03/2.25 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10075,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[10074])).
% 2.03/2.25 tff(10076,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[10075, 10073])).
% 2.03/2.25 tff(10077,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(10078,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[10077, 10076])).
% 2.03/2.25 tff(10079,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10078, 245, 308, 1103, 2824, 556])).
% 2.03/2.25 tff(10080,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(10081,plain,
% 2.03/2.25 (~b(elem!1, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10080, 7791, 308, 556])).
% 2.03/2.25 tff(10082,plain,
% 2.03/2.25 ((elem!1 = s(elem!1)) | r(elem!1, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1086, 32, 10081])).
% 2.03/2.25 tff(10083,plain,
% 2.03/2.25 (r(elem!1, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10082, 7735])).
% 2.03/2.25 tff(10084,plain,
% 2.03/2.25 (~r(elem!1, z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8955, 10083, 556, 308, 10070])).
% 2.03/2.25 tff(10085,plain,
% 2.03/2.25 (b(elem!1, z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[128, 10084, 3641])).
% 2.03/2.25 tff(10086,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10087,plain,
% 2.03/2.25 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(10088,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[10087])).
% 2.03/2.25 tff(10089,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[10088, 10086])).
% 2.03/2.25 tff(10090,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(10091,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[10090, 10089])).
% 2.03/2.25 tff(10092,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10091, 245, 10085, 308, 10072, 7791, 556])).
% 2.03/2.25 tff(10093,plain,((elem!1 = s(s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (elem!1 = z) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | r(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(10094,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[10093, 10068, 7316, 124, 105, 399, 10043])).
% 2.03/2.25 tff(10095,plain,
% 2.03/2.25 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8990, 10094, 9, 2338, 1, 88, 399])).
% 2.03/2.26 tff(10096,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[420, 10095, 10056, 7])).
% 2.03/2.26 tff(10097,plain,((~r(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(10098,plain,
% 2.03/2.26 (~r(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10097, 88, 1, 9, 399])).
% 2.03/2.26 tff(10099,plain,
% 2.03/2.26 (b(elem!1, s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2777, 10098, 2563])).
% 2.03/2.26 tff(10100,plain,
% 2.03/2.26 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7334, 10099, 7316, 10012])).
% 2.03/2.26 tff(10101,plain,
% 2.03/2.26 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[420, 10100, 7])).
% 2.03/2.26 tff(10102,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(z))) | (~b(s(z), elem!1)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10103,plain,
% 2.03/2.26 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10104,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, 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), s(z))) | (~b(s(z), elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10103])).
% 2.03/2.26 tff(10105,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, 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), s(z))) | (~b(s(z), elem!1)))),
% 2.03/2.26 inference(transitivity,[status(thm)],[10104, 10102])).
% 2.03/2.26 tff(10106,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(10107,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(z))) | (~b(s(z), elem!1))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10106, 10105])).
% 2.03/2.26 tff(10108,plain,
% 2.03/2.26 (~b(s(elem!1), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10107, 245, 308, 1103, 447])).
% 2.03/2.26 tff(10109,plain,
% 2.03/2.26 (r(s(elem!1), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[369, 10108, 358])).
% 2.03/2.26 tff(10110,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10111,plain,
% 2.03/2.26 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10112,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10111])).
% 2.03/2.26 tff(10113,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[10112, 10110])).
% 2.03/2.26 tff(10114,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(10115,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10114, 10113])).
% 2.03/2.26 tff(10116,plain,
% 2.03/2.26 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10115, 245, 308, 1103, 447, 2824])).
% 2.03/2.26 tff(10117,plain,
% 2.03/2.26 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[217, 10116])).
% 2.03/2.26 tff(10118,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8513, 10117, 10109, 406])).
% 2.03/2.26 tff(10119,plain,((~b(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(10120,plain,
% 2.03/2.26 (~b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10119, 10101, 348, 7316, 10099, 10012])).
% 2.03/2.26 tff(10121,plain,
% 2.03/2.26 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10080, 10099, 7316, 10012])).
% 2.03/2.26 tff(10122,plain,
% 2.03/2.26 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1263, 10121, 1])).
% 2.03/2.26 tff(10123,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), z)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10124,plain,
% 2.03/2.26 (((~b(s(elem!1), elem!1)) | (~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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10125,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(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(X0, 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), z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10124])).
% 2.03/2.26 tff(10126,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(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(X0, 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), z)))),
% 2.03/2.26 inference(transitivity,[status(thm)],[10125, 10123])).
% 2.03/2.26 tff(10127,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(10128,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), z))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10127, 10126])).
% 2.03/2.26 tff(10129,plain,
% 2.03/2.26 (~b(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10128, 245, 4105, 308, 1103])).
% 2.03/2.26 tff(10130,plain,
% 2.03/2.26 (r(s(elem!1), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1039, 10129])).
% 2.03/2.26 tff(10131,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10132,plain,
% 2.03/2.26 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, 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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10133,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10132])).
% 2.03/2.26 tff(10134,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.26 inference(transitivity,[status(thm)],[10133, 10131])).
% 2.03/2.26 tff(10135,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(10136,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10135, 10134])).
% 2.03/2.26 tff(10137,plain,
% 2.03/2.26 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10136, 245, 4105, 308, 1103, 2824])).
% 2.03/2.26 tff(10138,plain,
% 2.03/2.26 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2558, 10137])).
% 2.03/2.26 tff(10139,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4959, 10138, 10130, 1366])).
% 2.03/2.26 tff(10140,plain,((~b(z, elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(10141,plain,
% 2.03/2.26 (~b(z, elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10140, 10122, 7316, 10099, 10012])).
% 2.03/2.26 tff(10142,plain,
% 2.03/2.26 (r(z, elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[175, 10141, 118])).
% 2.03/2.26 tff(10143,plain,
% 2.03/2.26 (~(elem!1 = z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[123, 55])).
% 2.03/2.26 tff(10144,plain,
% 2.03/2.26 (r(elem!1, z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[128, 89, 10143])).
% 2.03/2.26 tff(10145,plain,
% 2.03/2.26 (r(z, elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[175, 90, 55])).
% 2.03/2.26 tff(10146,plain,
% 2.03/2.26 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[4881])).
% 2.03/2.26 tff(10147,plain,
% 2.03/2.26 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.03/2.26 inference(symmetry,[status(thm)],[10146])).
% 2.03/2.26 tff(10148,plain,
% 2.03/2.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[519, 2569])).
% 2.03/2.26 tff(10149,plain,
% 2.03/2.26 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[4881])).
% 2.03/2.26 tff(10150,plain,
% 2.03/2.26 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.03/2.26 inference(symmetry,[status(thm)],[10149])).
% 2.03/2.26 tff(10151,plain,
% 2.03/2.26 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.26 inference(symmetry,[status(thm)],[686])).
% 2.03/2.26 tff(10152,plain,
% 2.03/2.26 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.26 inference(transitivity,[status(thm)],[4885, 10151])).
% 2.03/2.26 tff(10153,plain,
% 2.03/2.26 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10152])).
% 2.03/2.26 tff(10154,plain,
% 2.03/2.26 (~(s(s(s(z))) = elem!1)),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[892, 10153])).
% 2.03/2.26 tff(10155,plain,
% 2.03/2.26 (r(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7257, 10154, 7255])).
% 2.03/2.26 tff(10156,plain,
% 2.03/2.26 (r(s(s(elem!1)), elem!1)),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10155, 10150])).
% 2.03/2.26 tff(10157,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[511, 10156])).
% 2.03/2.26 tff(10158,plain,
% 2.03/2.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[523, 32, 5017, 10157])).
% 2.03/2.26 tff(10159,plain,
% 2.03/2.26 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[4881])).
% 2.03/2.26 tff(10160,plain,
% 2.03/2.26 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.03/2.26 inference(symmetry,[status(thm)],[10159])).
% 2.03/2.26 tff(10161,plain,
% 2.03/2.26 ((~r(s(s(s(z))), z)) <=> (~r(s(s(elem!1)), z))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10160])).
% 2.03/2.26 tff(10162,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[830, 141, 289, 816, 979])).
% 2.03/2.26 tff(10163,plain,((~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(10164,plain,
% 2.03/2.26 (~r(s(s(s(z))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10163, 10155, 289])).
% 2.03/2.26 tff(10165,plain,
% 2.03/2.26 (~r(s(s(elem!1)), z)),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10164, 10161])).
% 2.03/2.26 tff(10166,plain,
% 2.03/2.26 (b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[542, 32, 258, 10165])).
% 2.03/2.26 tff(10167,plain,
% 2.03/2.26 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~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))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10168,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10167])).
% 2.03/2.26 tff(10169,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[10168, 544])).
% 2.03/2.26 tff(10170,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(10171,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10170, 10169])).
% 2.03/2.26 tff(10172,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10171, 245, 293, 6480, 10166, 10158])).
% 2.03/2.26 tff(10173,plain,((~(s(z) = elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(10174,plain,
% 2.03/2.26 (b(s(s(s(z))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10173, 2898, 111, 289, 10148])).
% 2.03/2.26 tff(10175,plain,
% 2.03/2.26 (b(s(s(elem!1)), elem!1)),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10174, 10147])).
% 2.03/2.26 tff(10176,plain,
% 2.03/2.26 (~(s(elem!1) = s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[396, 2569])).
% 2.03/2.26 tff(10177,plain,
% 2.03/2.26 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[4881])).
% 2.03/2.26 tff(10178,plain,
% 2.03/2.26 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(s(elem!1)))),
% 2.03/2.26 inference(symmetry,[status(thm)],[10177])).
% 2.03/2.26 tff(10179,plain,
% 2.03/2.26 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10178])).
% 2.03/2.26 tff(10180,plain,
% 2.03/2.26 (~(elem!1 = s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[4887, 10179])).
% 2.03/2.26 tff(10181,plain,
% 2.03/2.26 (~r(s(s(s(elem!1))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2875, 111, 289])).
% 2.03/2.26 tff(10182,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[37, 10181])).
% 2.03/2.26 tff(10183,plain,
% 2.03/2.26 (b(z, s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[197, 2324])).
% 2.03/2.26 tff(10184,plain,
% 2.03/2.26 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.26 inference(commutativity,[status(thm)],[])).
% 2.03/2.26 tff(10185,plain,
% 2.03/2.26 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.26 inference(symmetry,[status(thm)],[10184])).
% 2.03/2.26 tff(10186,plain,
% 2.03/2.26 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10185])).
% 2.03/2.26 tff(10187,plain,
% 2.03/2.26 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[5017, 10186])).
% 2.03/2.26 tff(10188,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.03/2.26 tff(10189,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 2.03/2.26 tff(10190,plain,
% 2.03/2.26 (((~![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(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(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10191,plain,
% 2.03/2.26 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(10192,plain,
% 2.03/2.26 (((~![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(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[10191])).
% 2.03/2.26 tff(10193,plain,
% 2.03/2.26 (((~![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(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[10192, 10190])).
% 2.03/2.26 tff(10194,plain,
% 2.03/2.26 ((~![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)))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(10195,plain,
% 2.03/2.26 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[10194, 10193])).
% 2.03/2.26 tff(10196,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10195, 141, 131, 10188, 10189])).
% 2.03/2.26 tff(10197,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(10198,plain,
% 2.03/2.26 (~r(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[10197, 10188, 131])).
% 2.03/2.26 tff(10199,plain,
% 2.03/2.26 (b(s(s(elem!1)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[542, 32, 258, 10198])).
% 2.03/2.26 tff(10200,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10201,plain,
% 2.03/2.27 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10202,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10201])).
% 2.03/2.27 tff(10203,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10202, 10200])).
% 2.03/2.27 tff(10204,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10205,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10204, 10203])).
% 2.03/2.27 tff(10206,plain,
% 2.03/2.27 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10205, 245, 235, 234, 10199])).
% 2.03/2.27 tff(10207,plain,
% 2.03/2.27 (((~![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))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10208,plain,
% 2.03/2.27 ((~![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))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10209,plain,
% 2.03/2.27 ((~![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)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10208, 10207])).
% 2.03/2.27 tff(10210,plain,
% 2.03/2.27 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10209, 32, 10206])).
% 2.03/2.27 tff(10211,plain,
% 2.03/2.27 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10210, 10187])).
% 2.03/2.27 tff(10212,plain,
% 2.03/2.27 (((~![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(elem!1))), 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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10213,plain,
% 2.03/2.27 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10214,plain,
% 2.03/2.27 (((~![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(elem!1))), 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(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10213])).
% 2.03/2.27 tff(10215,plain,
% 2.03/2.27 (((~![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(elem!1))), 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(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10214, 10212])).
% 2.03/2.27 tff(10216,plain,
% 2.03/2.27 ((~![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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10217,plain,
% 2.03/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10216, 10215])).
% 2.03/2.27 tff(10218,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10217, 141, 170, 10188, 10211])).
% 2.03/2.27 tff(10219,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(10220,plain,
% 2.03/2.27 (~r(elem!1, s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10219, 111, 10148, 10183, 10182, 131])).
% 2.03/2.27 tff(10221,plain,
% 2.03/2.27 (((~![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))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10222,plain,
% 2.03/2.27 ((~![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))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10223,plain,
% 2.03/2.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10222, 10221])).
% 2.03/2.27 tff(10224,plain,
% 2.03/2.27 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10223, 32, 10220])).
% 2.03/2.27 tff(10225,plain,
% 2.03/2.27 (b(elem!1, s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10224, 10180])).
% 2.03/2.27 tff(10226,plain,
% 2.03/2.27 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[4875])).
% 2.03/2.27 tff(10227,plain,
% 2.03/2.27 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10226])).
% 2.03/2.27 tff(10228,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[2628, 10226])).
% 2.03/2.27 tff(10229,plain,
% 2.03/2.27 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[4875])).
% 2.03/2.27 tff(10230,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[6811, 10229])).
% 2.03/2.27 tff(10231,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2326, 10230, 10228, 289, 1, 88])).
% 2.03/2.27 tff(10232,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~(s(z) = elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(10233,plain,
% 2.03/2.27 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10232, 2898, 1, 289, 88, 131])).
% 2.03/2.27 tff(10234,plain,
% 2.03/2.27 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10233, 10227])).
% 2.03/2.27 tff(10235,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[151, 10234, 2562])).
% 2.03/2.27 tff(10236,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[4881])).
% 2.03/2.27 tff(10237,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.27 inference(symmetry,[status(thm)],[10236])).
% 2.03/2.27 tff(10238,plain,
% 2.03/2.27 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[4875])).
% 2.03/2.27 tff(10239,plain,
% 2.03/2.27 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10238])).
% 2.03/2.27 tff(10240,plain,
% 2.03/2.27 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10239, 901])).
% 2.03/2.27 tff(10241,plain,
% 2.03/2.27 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.03/2.27 inference(symmetry,[status(thm)],[10240])).
% 2.03/2.27 tff(10242,plain,
% 2.03/2.27 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10241])).
% 2.03/2.27 tff(10243,plain,
% 2.03/2.27 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[704, 10242])).
% 2.03/2.27 tff(10244,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[4881])).
% 2.03/2.27 tff(10245,plain,
% 2.03/2.27 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10244])).
% 2.03/2.27 tff(10246,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.03/2.27 tff(10247,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10248,plain,
% 2.03/2.27 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(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)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10249,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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(X0, 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))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10248])).
% 2.03/2.27 tff(10250,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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(X0, 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)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10249, 10247])).
% 2.03/2.27 tff(10251,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10252,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10251, 10250])).
% 2.03/2.27 tff(10253,plain,
% 2.03/2.27 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10252, 245, 2824, 446])).
% 2.03/2.27 tff(10254,plain,
% 2.03/2.27 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10253, 10246])).
% 2.03/2.27 tff(10255,plain,
% 2.03/2.27 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10254, 10245])).
% 2.03/2.27 tff(10256,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 2.03/2.27 tff(10257,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), introduced(assumption)).
% 2.03/2.27 tff(10258,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 2.03/2.27 tff(10259,plain,
% 2.03/2.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10260,plain,
% 2.03/2.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10261,plain,
% 2.03/2.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10260, 10259])).
% 2.03/2.27 tff(10262,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10261, 32, 10258, 10257, 10256])).
% 2.03/2.27 tff(10263,plain,(r(s(s(s(s(elem!1)))), s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(10264,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10263, 10255, 10243])).
% 2.03/2.27 tff(10265,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10264, 10237])).
% 2.03/2.27 tff(10266,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10267,plain,
% 2.03/2.27 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10268,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10267])).
% 2.03/2.27 tff(10269,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10268, 10266])).
% 2.03/2.27 tff(10270,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10271,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10270, 10269])).
% 2.03/2.27 tff(10272,plain,
% 2.03/2.27 ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10271, 245, 308, 446])).
% 2.03/2.27 tff(10273,plain,
% 2.03/2.27 (~b(s(elem!1), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10272, 10246])).
% 2.03/2.27 tff(10274,plain,
% 2.03/2.27 (r(s(elem!1), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[484, 32, 481, 10273])).
% 2.03/2.27 tff(10275,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10276,plain,
% 2.03/2.27 (((~b(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), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(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(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10277,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10276])).
% 2.03/2.27 tff(10278,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10277, 10275])).
% 2.03/2.27 tff(10279,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10280,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10279, 10278])).
% 2.03/2.27 tff(10281,plain,
% 2.03/2.27 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10280, 245, 308, 2824, 446])).
% 2.03/2.27 tff(10282,plain,
% 2.03/2.27 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10281, 10246])).
% 2.03/2.27 tff(10283,plain,
% 2.03/2.27 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[420, 10282, 164])).
% 2.03/2.27 tff(10284,plain,
% 2.03/2.27 (((~![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(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10285,plain,
% 2.03/2.27 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10286,plain,
% 2.03/2.27 (((~![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(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10285])).
% 2.03/2.27 tff(10287,plain,
% 2.03/2.27 (((~![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(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10286, 10284])).
% 2.03/2.27 tff(10288,plain,
% 2.03/2.27 ((~![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))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10289,plain,
% 2.03/2.27 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10288, 10287])).
% 2.03/2.27 tff(10290,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10289, 141, 10283, 10274, 10265])).
% 2.03/2.27 tff(10291,plain,((~b(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(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(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(10292,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10291, 10235, 10225, 10176, 7, 10175, 2898, 7316])).
% 2.03/2.27 tff(10293,plain,((~(s(z) = elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(10294,plain,
% 2.03/2.27 (~(s(z) = elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10293, 10145, 88, 1, 2562, 10144])).
% 2.03/2.27 tff(10295,plain,
% 2.03/2.27 (~(z = elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7687, 7685, 7316])).
% 2.03/2.27 tff(10296,plain,
% 2.03/2.27 (~(s(z) = s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[57, 10295])).
% 2.03/2.27 tff(10297,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8737, 10296, 90, 1, 89])).
% 2.03/2.27 tff(10298,plain,
% 2.03/2.27 (r(z, elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[175, 10295, 90])).
% 2.03/2.27 tff(10299,plain,
% 2.03/2.27 (~(elem!1 = z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[123, 10295])).
% 2.03/2.27 tff(10300,plain,
% 2.03/2.27 (r(elem!1, z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[128, 10299, 89])).
% 2.03/2.27 tff(10301,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2560, 88, 89, 90, 1])).
% 2.03/2.27 tff(10302,plain,
% 2.03/2.27 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[6474, 89, 1, 90])).
% 2.03/2.27 tff(10303,plain,
% 2.03/2.27 (~(s(z) = elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10293, 88, 289, 1, 10302, 131])).
% 2.03/2.27 tff(10304,plain,
% 2.03/2.27 (b(s(z), elem!1)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[389, 10303, 5511])).
% 2.03/2.27 tff(10305,plain,
% 2.03/2.27 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2567, 10302])).
% 2.03/2.27 tff(10306,plain,
% 2.03/2.27 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1957, 10305])).
% 2.03/2.27 tff(10307,plain,
% 2.03/2.27 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.03/2.27 inference(symmetry,[status(thm)],[7112])).
% 2.03/2.27 tff(10308,plain,
% 2.03/2.27 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10307])).
% 2.03/2.27 tff(10309,plain,
% 2.03/2.27 (s(s(z)) = s(s(elem!1))),
% 2.03/2.27 inference(transitivity,[status(thm)],[586, 10308, 157])).
% 2.03/2.27 tff(10310,plain,
% 2.03/2.27 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10309])).
% 2.03/2.27 tff(10311,plain,
% 2.03/2.27 (s(z) = s(elem!1)),
% 2.03/2.27 inference(transitivity,[status(thm)],[591, 10310, 155])).
% 2.03/2.27 tff(10312,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9, 10311])).
% 2.03/2.27 tff(10313,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(10314,plain,
% 2.03/2.27 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10313, 9])).
% 2.03/2.27 tff(10315,plain,
% 2.03/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10316,plain,
% 2.03/2.27 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10317,plain,
% 2.03/2.27 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10316])).
% 2.03/2.28 tff(10318,plain,
% 2.03/2.28 (((~![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(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10317, 10315])).
% 2.03/2.28 tff(10319,plain,
% 2.03/2.28 ((~![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(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10320,plain,
% 2.03/2.28 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10319, 10318])).
% 2.03/2.28 tff(10321,plain,
% 2.03/2.28 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10320, 141, 170, 816])).
% 2.03/2.28 tff(10322,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 2.03/2.28 tff(10323,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7120, 32, 10322, 10321])).
% 2.03/2.28 tff(10324,plain,
% 2.03/2.28 (~r(s(s(s(z))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10163, 816, 289])).
% 2.03/2.28 tff(10325,plain,
% 2.03/2.28 (b(s(s(s(z))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7060, 10324])).
% 2.03/2.28 tff(10326,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10327,plain,
% 2.03/2.28 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10328,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10327])).
% 2.03/2.28 tff(10329,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10328, 10326])).
% 2.03/2.28 tff(10330,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10331,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10330, 10329])).
% 2.03/2.28 tff(10332,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10331, 245, 293, 6480, 10325, 10323])).
% 2.03/2.28 tff(10333,plain,((~r(s(s(s(z))), elem!1)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10334,plain,
% 2.03/2.28 (~r(s(s(s(z))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10333, 111, 10314, 289])).
% 2.03/2.28 tff(10335,plain,
% 2.03/2.28 (~(elem!1 = s(z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10303, 5254])).
% 2.03/2.28 tff(10336,plain,
% 2.03/2.28 (b(elem!1, s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[281, 10335, 2100])).
% 2.03/2.28 tff(10337,plain,
% 2.03/2.28 (~(s(elem!1) = s(s(elem!1)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[396, 10306])).
% 2.03/2.28 tff(10338,plain,
% 2.03/2.28 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[519, 10306])).
% 2.03/2.28 tff(10339,plain,
% 2.03/2.28 (~b(s(elem!1), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[5723, 245, 10336, 7316, 10304])).
% 2.03/2.28 tff(10340,plain,
% 2.03/2.28 (r(s(elem!1), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[369, 10339, 348])).
% 2.03/2.28 tff(10341,plain,
% 2.03/2.28 (s(s(s(s(z)))) = s(elem!1)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[862])).
% 2.03/2.28 tff(10342,plain,
% 2.03/2.28 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10341])).
% 2.03/2.28 tff(10343,plain,
% 2.03/2.28 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.03/2.28 inference(symmetry,[status(thm)],[10342])).
% 2.03/2.28 tff(10344,plain,
% 2.03/2.28 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10343])).
% 2.03/2.28 tff(10345,plain,
% 2.03/2.28 (b(s(s(s(s(s(z))))), z) <=> b(s(s(elem!1)), z)),
% 2.03/2.28 inference(symmetry,[status(thm)],[10344])).
% 2.03/2.28 tff(10346,plain,
% 2.03/2.28 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[771])).
% 2.03/2.28 tff(10347,plain,
% 2.03/2.28 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(z))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10346, 686])).
% 2.03/2.28 tff(10348,plain,
% 2.03/2.28 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = elem!1)),
% 2.03/2.28 inference(transitivity,[status(thm)],[10347, 10151])).
% 2.03/2.28 tff(10349,plain,
% 2.03/2.28 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10348])).
% 2.03/2.28 tff(10350,plain,
% 2.03/2.28 (~(s(s(s(z))) = elem!1)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[704, 10349])).
% 2.03/2.28 tff(10351,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[862, 10350])).
% 2.03/2.28 tff(10352,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10353,plain,
% 2.03/2.28 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10352, 862])).
% 2.03/2.28 tff(10354,plain,
% 2.03/2.28 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10343])).
% 2.03/2.28 tff(10355,plain,
% 2.03/2.28 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10354])).
% 2.03/2.28 tff(10356,plain,
% 2.03/2.28 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 2.03/2.28 inference(commutativity,[status(thm)],[])).
% 2.03/2.28 tff(10357,plain,
% 2.03/2.28 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.03/2.28 inference(symmetry,[status(thm)],[10356])).
% 2.03/2.28 tff(10358,plain,
% 2.03/2.28 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10357])).
% 2.03/2.28 tff(10359,plain,
% 2.03/2.28 (~(s(s(elem!1)) = s(elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[481, 10358])).
% 2.03/2.28 tff(10360,plain,
% 2.03/2.28 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10343])).
% 2.03/2.28 tff(10361,plain,
% 2.03/2.28 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.03/2.28 inference(symmetry,[status(thm)],[10360])).
% 2.03/2.28 tff(10362,plain,
% 2.03/2.28 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(elem!1)), s(elem!1)))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10361])).
% 2.03/2.28 tff(10363,plain,
% 2.03/2.28 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10343])).
% 2.03/2.28 tff(10364,plain,
% 2.03/2.28 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10363])).
% 2.03/2.28 tff(10365,plain,
% 2.03/2.28 (~b(s(s(elem!1)), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[5519, 245, 301, 447, 446])).
% 2.03/2.28 tff(10366,plain,
% 2.03/2.28 (~b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10365, 10364])).
% 2.03/2.28 tff(10367,plain,
% 2.03/2.28 (r(s(s(s(s(s(z))))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[809, 10366])).
% 2.03/2.28 tff(10368,plain,
% 2.03/2.28 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1003, 10367, 998])).
% 2.03/2.28 tff(10369,plain,
% 2.03/2.28 (~r(s(s(elem!1)), s(elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10368, 10362])).
% 2.03/2.28 tff(10370,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), 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(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10371,plain,
% 2.03/2.28 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10372,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10371])).
% 2.03/2.28 tff(10373,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10372, 10370])).
% 2.03/2.28 tff(10374,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10375,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10374, 10373])).
% 2.03/2.28 tff(10376,plain,
% 2.03/2.28 (~b(s(s(elem!1)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10375, 245, 301, 308, 447, 446])).
% 2.03/2.28 tff(10377,plain,
% 2.03/2.28 (((~![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)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10378,plain,
% 2.03/2.28 ((~![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)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10379,plain,
% 2.03/2.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10378, 10377])).
% 2.03/2.28 tff(10380,plain,
% 2.03/2.28 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10379, 32, 10376])).
% 2.03/2.28 tff(10381,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10380, 10369, 10359])).
% 2.03/2.28 tff(10382,plain,((~b(s(s(elem!1)), elem!1)) | (~(s(s(s(z))) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10383,plain,
% 2.03/2.28 (~b(s(s(elem!1)), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10382, 862, 481, 998, 301, 447, 308])).
% 2.03/2.28 tff(10384,plain,
% 2.03/2.28 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10383, 10355])).
% 2.03/2.28 tff(10385,plain,
% 2.03/2.28 (r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[787, 10384, 10353])).
% 2.03/2.28 tff(10386,plain,
% 2.03/2.28 (~r(s(s(s(s(s(z))))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[6809, 10385, 131])).
% 2.03/2.28 tff(10387,plain,
% 2.03/2.28 (b(s(s(s(s(s(z))))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[738, 10386])).
% 2.03/2.28 tff(10388,plain,
% 2.03/2.28 (b(s(s(elem!1)), z)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10387, 10345])).
% 2.03/2.28 tff(10389,plain,
% 2.03/2.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10343])).
% 2.03/2.28 tff(10390,plain,
% 2.03/2.28 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.03/2.28 inference(symmetry,[status(thm)],[10389])).
% 2.03/2.28 tff(10391,plain,
% 2.03/2.28 (r(s(s(elem!1)), elem!1)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10385, 10390])).
% 2.03/2.28 tff(10392,plain,
% 2.03/2.28 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[510, 141, 170, 10391])).
% 2.03/2.28 tff(10393,plain,
% 2.03/2.28 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[523, 32, 5017, 10392])).
% 2.03/2.28 tff(10394,plain,
% 2.03/2.28 ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[549, 245, 235, 234])).
% 2.03/2.28 tff(10395,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10394, 10393, 10388])).
% 2.03/2.28 tff(10396,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z)) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10397,plain,
% 2.03/2.28 (~(s(s(s(z))) = elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10396, 10340, 10182, 10338, 111, 131, 10337, 10183, 10336, 10304, 7316])).
% 2.03/2.28 tff(10398,plain,
% 2.03/2.28 (b(s(s(s(z))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7257, 10397, 10334])).
% 2.03/2.28 tff(10399,plain,
% 2.03/2.28 (~b(s(s(s(z))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[884, 245, 10336, 10304, 10398])).
% 2.03/2.28 tff(10400,plain,
% 2.03/2.28 (r(s(s(s(z))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[895, 32, 892, 10399])).
% 2.03/2.28 tff(10401,plain,
% 2.03/2.28 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10402,plain,
% 2.03/2.28 ((~![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))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10403,plain,
% 2.03/2.28 ((~![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)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10402, 10401])).
% 2.03/2.28 tff(10404,plain,
% 2.03/2.28 (~r(s(s(s(z))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10403, 141, 10340, 10400])).
% 2.03/2.28 tff(10405,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), 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(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10406,plain,
% 2.03/2.28 (((~b(s(z), elem!1)) | (~b(s(s(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(elem!1), 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(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10407,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10406])).
% 2.03/2.28 tff(10408,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10407, 10405])).
% 2.03/2.28 tff(10409,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10410,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10409, 10408])).
% 2.03/2.28 tff(10411,plain,
% 2.03/2.28 (~b(s(s(s(z))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10410, 245, 10336, 7316, 10304, 10398])).
% 2.03/2.28 tff(10412,plain,
% 2.03/2.28 (((~![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)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10413,plain,
% 2.03/2.28 ((~![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)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10414,plain,
% 2.03/2.28 ((~![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))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10413, 10412])).
% 2.03/2.28 tff(10415,plain,
% 2.03/2.28 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10414, 32, 10411])).
% 2.03/2.28 tff(10416,plain,
% 2.03/2.28 (s(s(s(z))) = s(elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10415, 10404])).
% 2.03/2.28 tff(10417,plain,
% 2.03/2.28 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10416])).
% 2.03/2.28 tff(10418,plain,
% 2.03/2.28 (~r(s(s(s(z))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[985, 10400, 220])).
% 2.03/2.28 tff(10419,plain,
% 2.03/2.28 (b(s(s(s(z))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7060, 10418])).
% 2.03/2.28 tff(10420,plain,
% 2.03/2.28 (b(s(elem!1), z)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10419, 10417])).
% 2.03/2.28 tff(10421,plain,
% 2.03/2.28 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[299, 245, 10183, 10182, 10420])).
% 2.03/2.28 tff(10422,plain,
% 2.03/2.28 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[353, 10421, 10306])).
% 2.03/2.28 tff(10423,plain,
% 2.03/2.28 (~b(s(z), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[5820, 245, 10336, 7316, 10304])).
% 2.03/2.28 tff(10424,plain,
% 2.03/2.28 (r(s(z), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[440, 10423, 9])).
% 2.03/2.28 tff(10425,plain,
% 2.03/2.28 (~r(s(s(s(elem!1))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3350, 141, 10422, 10424])).
% 2.03/2.28 tff(10426,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[265, 10425])).
% 2.03/2.28 tff(10427,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10428,plain,
% 2.03/2.28 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10429,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10428])).
% 2.03/2.28 tff(10430,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10429, 10427])).
% 2.03/2.28 tff(10431,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10432,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10431, 10430])).
% 2.03/2.28 tff(10433,plain,
% 2.03/2.28 (~b(elem!1, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10432, 245, 10336, 10304, 10426])).
% 2.03/2.28 tff(10434,plain,
% 2.03/2.28 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1724, 10433, 1673])).
% 2.03/2.28 tff(10435,plain,
% 2.03/2.28 (~r(elem!1, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2762, 10434, 10422])).
% 2.03/2.28 tff(10436,plain,
% 2.03/2.28 (b(elem!1, s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2777, 10435, 2563])).
% 2.03/2.28 tff(10437,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10115, 245, 7316, 10436, 10304, 10301])).
% 2.03/2.28 tff(10438,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7334, 10301, 7316, 10436])).
% 2.03/2.28 tff(10439,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[420, 10438, 7])).
% 2.03/2.28 tff(10440,plain,
% 2.03/2.28 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2296, 141, 10424, 10439])).
% 2.03/2.28 tff(10441,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[217, 10440, 10437])).
% 2.03/2.28 tff(10442,plain,(b(s(s(s(elem!1))), elem!1) | b(elem!1, z) | b(z, elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(elem!1, z)) | (s(z) = s(elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10443,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10442, 9462, 90, 1, 89, 10300, 10296, 10298])).
% 2.03/2.28 tff(10444,plain,
% 2.03/2.28 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8124, 2338])).
% 2.03/2.28 tff(10445,plain,
% 2.03/2.28 (~r(z, s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3688, 1368, 289])).
% 2.03/2.28 tff(10446,plain,
% 2.03/2.28 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1992, 10445])).
% 2.03/2.28 tff(10447,plain,
% 2.03/2.28 (~r(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[5214, 1368, 131])).
% 2.03/2.28 tff(10448,plain,
% 2.03/2.28 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2558, 10447])).
% 2.03/2.28 tff(10449,plain,
% 2.03/2.28 (~b(z, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2066, 245, 2197, 1276, 1943])).
% 2.03/2.28 tff(10450,plain,
% 2.03/2.28 (r(z, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[197, 10449])).
% 2.03/2.28 tff(10451,plain,
% 2.03/2.28 (~r(elem!1, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2078, 10450, 289])).
% 2.03/2.28 tff(10452,plain,
% 2.03/2.28 (b(elem!1, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1724, 10451, 3600])).
% 2.03/2.28 tff(10453,plain,
% 2.03/2.28 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3318, 10452, 2824, 1276])).
% 2.03/2.28 tff(10454,plain,
% 2.03/2.28 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[110, 10453, 102])).
% 2.03/2.28 tff(10455,plain,
% 2.03/2.28 (~b(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2032, 245, 2197, 1276, 1943])).
% 2.03/2.28 tff(10456,plain,
% 2.03/2.28 (r(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[37, 10455])).
% 2.03/2.28 tff(10457,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[179, 141, 289, 10456, 10454])).
% 2.03/2.28 tff(10458,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10459,plain,
% 2.03/2.28 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10458, 10448, 96, 289, 10446, 2824])).
% 2.03/2.28 tff(10460,plain,
% 2.03/2.28 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1239, 10459, 1304])).
% 2.03/2.28 tff(10461,plain,
% 2.03/2.28 (~b(elem!1, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8901, 1427, 1, 2338, 2824])).
% 2.03/2.28 tff(10462,plain,
% 2.03/2.28 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1724, 10461, 1673])).
% 2.03/2.28 tff(10463,plain,
% 2.03/2.28 (~r(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[4128, 10462, 131])).
% 2.03/2.28 tff(10464,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[37, 10463])).
% 2.03/2.28 tff(10465,plain,
% 2.03/2.28 (~r(z, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2078, 10462, 289])).
% 2.03/2.28 tff(10466,plain,
% 2.03/2.28 (b(z, s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[197, 10465])).
% 2.03/2.28 tff(10467,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10468,plain,
% 2.03/2.28 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~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(s(elem!1)))), z)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10469,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10468])).
% 2.03/2.28 tff(10470,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10469, 10467])).
% 2.03/2.28 tff(10471,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10472,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10471, 10470])).
% 2.03/2.28 tff(10473,plain,
% 2.03/2.28 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10472, 245, 1427, 10466, 10464, 2824])).
% 2.03/2.29 tff(10474,plain,
% 2.03/2.29 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10473, 10448])).
% 2.03/2.29 tff(10475,plain,
% 2.03/2.29 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1320, 10474, 1312])).
% 2.03/2.29 tff(10476,plain,
% 2.03/2.29 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2756, 10475, 10462])).
% 2.03/2.29 tff(10477,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10093, 10476, 7316, 399, 105, 3641, 289])).
% 2.03/2.29 tff(10478,plain,
% 2.03/2.29 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1263, 10477, 1])).
% 2.03/2.29 tff(10479,plain,
% 2.03/2.29 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2357, 10478, 10460])).
% 2.03/2.29 tff(10480,plain,
% 2.03/2.29 (~r(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1376, 10478, 1368])).
% 2.03/2.29 tff(10481,plain,
% 2.03/2.29 (b(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2777, 10480, 2563])).
% 2.03/2.29 tff(10482,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2334, 10481, 7316, 1427])).
% 2.03/2.29 tff(10483,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2091, 32, 10482, 10479, 10444])).
% 2.03/2.29 tff(10484,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (elem!1 = z) | (~r(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10485,plain,
% 2.03/2.29 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10484, 10443, 1, 10305, 10299, 10298, 10297, 10300])).
% 2.03/2.29 tff(10486,plain,
% 2.03/2.29 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1432, 10485, 10305])).
% 2.03/2.29 tff(10487,plain,
% 2.03/2.29 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2849, 10486, 10443, 10297])).
% 2.03/2.29 tff(10488,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1239, 10487, 1304])).
% 2.03/2.29 tff(10489,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7667, 10486, 7316, 10297])).
% 2.03/2.29 tff(10490,plain,
% 2.03/2.29 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1263, 10489, 1])).
% 2.03/2.29 tff(10491,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10492,plain,
% 2.03/2.29 (((~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)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10493,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10492])).
% 2.03/2.29 tff(10494,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(elem!1, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10493, 10491])).
% 2.03/2.29 tff(10495,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10496,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10495, 10494])).
% 2.03/2.29 tff(10497,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10496, 245, 1287, 1390, 308, 1427, 2824])).
% 2.03/2.29 tff(10498,plain,((~b(elem!1, s(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)) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10499,plain,
% 2.03/2.29 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10498, 10486, 7316, 10443, 10297])).
% 2.03/2.29 tff(10500,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[353, 10499, 10306])).
% 2.03/2.29 tff(10501,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2377, 10500, 10490, 10488])).
% 2.03/2.29 tff(10502,plain,(b(s(z), z) | (s(elem!1) = s(s(s(s(elem!1))))) | b(z, elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10503,plain,
% 2.03/2.29 (b(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10502, 90, 89, 1])).
% 2.03/2.29 tff(10504,plain,
% 2.03/2.29 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1143, 170, 619])).
% 2.03/2.29 tff(10505,plain,
% 2.03/2.29 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1133, 10504])).
% 2.03/2.29 tff(10506,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1119, 245, 235, 6480, 355, 10505])).
% 2.03/2.29 tff(10507,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10508,plain,
% 2.03/2.29 (~b(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10507, 170, 355, 289, 619])).
% 2.03/2.29 tff(10509,plain,
% 2.03/2.29 (r(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[197, 10508])).
% 2.03/2.29 tff(10510,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[187, 141, 289, 170, 10509])).
% 2.03/2.29 tff(10511,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~b(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10512,plain,
% 2.03/2.29 (~r(s(z), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10511, 10503, 111, 10145])).
% 2.03/2.29 tff(10513,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[389, 10512, 10294, 7680])).
% 2.03/2.29 tff(10514,plain,(b(z, elem!1) | b(s(z), elem!1) | b(s(s(s(elem!1))), elem!1) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | b(elem!1, z) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10515,plain,
% 2.03/2.29 (b(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10514, 10141, 88, 1, 7790, 10120, 118])).
% 2.03/2.29 tff(10516,plain,
% 2.03/2.29 (b(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9465, 10142, 10120, 10515])).
% 2.03/2.29 tff(10517,plain,
% 2.03/2.29 (~r(s(z), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10511, 10516, 111, 10142])).
% 2.03/2.29 tff(10518,plain,
% 2.03/2.29 (s(z) = elem!1),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[389, 10517, 10120])).
% 2.03/2.29 tff(10519,plain,
% 2.03/2.29 (elem!1 = s(z)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10518, 338])).
% 2.03/2.29 tff(10520,plain,
% 2.03/2.29 (s(s(z)) = s(elem!1)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10518])).
% 2.03/2.29 tff(10521,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10520])).
% 2.03/2.29 tff(10522,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10521])).
% 2.03/2.29 tff(10523,plain,
% 2.03/2.29 (~b(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7375, 10101, 7316, 10012, 2338, 10099, 1304])).
% 2.03/2.29 tff(10524,plain,
% 2.03/2.29 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1724, 10523, 1673])).
% 2.03/2.29 tff(10525,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10080, 1103, 7316, 10012])).
% 2.03/2.29 tff(10526,plain,
% 2.03/2.29 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1263, 10525, 1])).
% 2.03/2.29 tff(10527,plain,
% 2.03/2.29 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7334, 1103, 7316, 10012])).
% 2.03/2.29 tff(10528,plain,
% 2.03/2.29 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[420, 10527, 7])).
% 2.03/2.29 tff(10529,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[415, 371, 10528])).
% 2.03/2.29 tff(10530,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1239, 10529, 1304])).
% 2.03/2.29 tff(10531,plain,
% 2.03/2.29 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2058, 141, 371, 10528])).
% 2.03/2.29 tff(10532,plain,
% 2.03/2.29 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1320, 10531, 1312])).
% 2.03/2.29 tff(10533,plain,
% 2.03/2.29 (~b(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8982, 10532, 8920, 10530])).
% 2.03/2.29 tff(10534,plain,
% 2.03/2.29 (r(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1992, 10533])).
% 2.03/2.29 tff(10535,plain,
% 2.03/2.29 (~r(z, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5050, 10534, 10526])).
% 2.03/2.29 tff(10536,plain,
% 2.03/2.29 (b(z, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[644, 10535])).
% 2.03/2.29 tff(10537,plain,
% 2.03/2.29 (~b(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9046, 245, 7316, 1103, 10536])).
% 2.03/2.29 tff(10538,plain,
% 2.03/2.29 (r(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[128, 10537, 3641])).
% 2.03/2.29 tff(10539,plain,
% 2.03/2.29 (~r(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3608, 10538, 2070])).
% 2.03/2.29 tff(10540,plain,
% 2.03/2.29 (~r(s(elem!1), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5306, 10534, 10526])).
% 2.03/2.29 tff(10541,plain,
% 2.03/2.29 (b(s(elem!1), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1039, 10540])).
% 2.03/2.29 tff(10542,plain,
% 2.03/2.29 (~b(z, elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9053, 245, 7316, 1103, 10536])).
% 2.03/2.29 tff(10543,plain,
% 2.03/2.29 (b(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10502, 10537, 10542, 1])).
% 2.03/2.29 tff(10544,plain,
% 2.03/2.29 (~b(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[379, 10543, 8920, 358, 10541, 371])).
% 2.03/2.29 tff(10545,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[197, 10544, 10539])).
% 2.03/2.29 tff(10546,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(z)) | (~r(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (elem!1 = z) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10547,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10546, 10524, 348, 1, 124, 10099])).
% 2.03/2.29 tff(10548,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[353, 10547, 2338])).
% 2.03/2.29 tff(10549,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10548, 10522])).
% 2.03/2.29 tff(10550,plain,
% 2.03/2.29 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10520, 10518])).
% 2.03/2.29 tff(10551,plain,
% 2.03/2.29 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10550])).
% 2.03/2.29 tff(10552,plain,
% 2.03/2.29 (b(s(s(z)), s(z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[7316, 10551])).
% 2.03/2.29 tff(10553,plain,
% 2.03/2.29 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[4278])).
% 2.03/2.29 tff(10554,plain,
% 2.03/2.29 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10553])).
% 2.03/2.29 tff(10555,plain,
% 2.03/2.29 (b(z, s(s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[838, 10554])).
% 2.03/2.29 tff(10556,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 2.03/2.29 tff(10557,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 2.03/2.29 tff(10558,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10559,plain,
% 2.03/2.29 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10560,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10559])).
% 2.03/2.29 tff(10561,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10560, 10558])).
% 2.03/2.29 tff(10562,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10563,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10562, 10561])).
% 2.03/2.29 tff(10564,plain,
% 2.03/2.29 (~b(z, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10563, 245, 234, 355, 10557, 10556])).
% 2.03/2.29 tff(10565,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10564, 10555])).
% 2.03/2.29 tff(10566,plain,((~b(z, s(elem!1))) | (~(elem!1 = s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10567,plain,
% 2.03/2.29 (~b(z, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10566, 10552, 10516, 8920, 10549, 10519])).
% 2.03/2.29 tff(10568,plain,
% 2.03/2.29 (r(z, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[644, 10567])).
% 2.03/2.29 tff(10569,plain,
% 2.03/2.29 (~r(s(s(s(s(elem!1)))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1350, 10568, 10101])).
% 2.03/2.29 tff(10570,plain,
% 2.03/2.29 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2558, 10569])).
% 2.03/2.29 tff(10571,plain,
% 2.03/2.29 (~r(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2078, 10142, 10524])).
% 2.03/2.29 tff(10572,plain,
% 2.03/2.29 (b(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[197, 10571])).
% 2.03/2.29 tff(10573,plain,
% 2.03/2.29 (~r(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3674, 10568, 10101])).
% 2.03/2.29 tff(10574,plain,
% 2.03/2.29 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1992, 10573])).
% 2.03/2.29 tff(10575,plain,
% 2.03/2.29 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10458, 10574, 96, 10012, 10142, 10570])).
% 2.03/2.29 tff(10576,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1239, 10575, 1304])).
% 2.03/2.29 tff(10577,plain,
% 2.03/2.29 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3538, 10576, 111])).
% 2.03/2.29 tff(10578,plain,
% 2.03/2.29 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1432, 10577, 399])).
% 2.03/2.29 tff(10579,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10580,plain,
% 2.03/2.29 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10581,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10580])).
% 2.03/2.29 tff(10582,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10581, 10579])).
% 2.03/2.29 tff(10583,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10584,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10583, 10582])).
% 2.03/2.29 tff(10585,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10584, 245, 10515, 10548, 10578, 10099, 10572, 10570])).
% 2.03/2.29 tff(10586,plain,(b(s(s(s(elem!1))), elem!1) | (elem!1 = s(s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10587,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10586, 399, 1, 9])).
% 2.03/2.29 tff(10588,plain,
% 2.03/2.29 (~b(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8901, 1427, 1, 10012, 2338])).
% 2.03/2.29 tff(10589,plain,
% 2.03/2.29 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1724, 10588, 1673])).
% 2.03/2.29 tff(10590,plain,
% 2.03/2.29 (~r(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2078, 289, 10589])).
% 2.03/2.29 tff(10591,plain,
% 2.03/2.29 (b(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[197, 10590])).
% 2.03/2.29 tff(10592,plain,
% 2.03/2.29 (~b(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[4562, 10591, 8920, 1427])).
% 2.03/2.29 tff(10593,plain,
% 2.03/2.29 (r(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[128, 10592, 3641])).
% 2.03/2.29 tff(10594,plain,
% 2.03/2.29 (~r(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10039, 10593, 7316, 10012, 7, 1304, 1673, 399, 8920])).
% 2.03/2.29 tff(10595,plain,
% 2.03/2.29 (b(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2777, 10594, 2563])).
% 2.03/2.29 tff(10596,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10546, 10595, 358, 1, 3641, 10589])).
% 2.03/2.29 tff(10597,plain,
% 2.03/2.29 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10484, 10593, 1, 10012, 3641, 1427, 399, 289])).
% 2.03/2.29 tff(10598,plain,
% 2.03/2.29 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1432, 10597, 399])).
% 2.03/2.29 tff(10599,plain,
% 2.03/2.29 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10498, 10598, 7316, 10012, 1427])).
% 2.03/2.29 tff(10600,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[353, 10599, 10596, 2338])).
% 2.03/2.29 tff(10601,plain,((~r(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(s(elem!1))))) | (elem!1 = z) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10602,plain,
% 2.03/2.29 (~r(z, elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10601, 10587, 348, 1, 124, 399])).
% 2.03/2.29 tff(10603,plain,
% 2.03/2.29 (b(z, elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[175, 10602, 118])).
% 2.03/2.29 tff(10604,plain,
% 2.03/2.29 (~b(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8118, 10603, 7316, 7790, 1, 9, 2338])).
% 2.03/2.29 tff(10605,plain,
% 2.03/2.29 (r(elem!1, z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[128, 10604, 124])).
% 2.03/2.29 tff(10606,plain,
% 2.03/2.29 (~r(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10039, 10605, 7316, 10012, 7, 1304, 1673, 399, 8920])).
% 2.03/2.29 tff(10607,plain,
% 2.03/2.29 (b(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2777, 10606, 2563])).
% 2.03/2.29 tff(10608,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10080, 10607, 7316, 10012])).
% 2.03/2.29 tff(10609,plain,
% 2.03/2.29 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10140, 10607, 7316, 10603, 10012])).
% 2.03/2.29 tff(10610,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1263, 10609, 10608, 1])).
% 2.03/2.29 tff(10611,plain,((elem!1 = s(s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10612,plain,
% 2.03/2.29 (s(z) = s(elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10611, 10019, 1])).
% 2.03/2.29 tff(10613,plain,
% 2.03/2.29 (z = elem!1),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[57, 10612])).
% 2.03/2.29 tff(10614,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10613])).
% 2.03/2.29 tff(10615,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[8920, 10614])).
% 2.03/2.29 tff(10616,plain,
% 2.03/2.29 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1957, 10019])).
% 2.03/2.29 tff(10617,plain,
% 2.03/2.29 (~b(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8901, 10615, 1, 10012, 10616])).
% 2.03/2.29 tff(10618,plain,
% 2.03/2.29 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1724, 10617, 1673])).
% 2.03/2.29 tff(10619,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2762, 8715, 10618])).
% 2.03/2.29 tff(10620,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[353, 10619, 10616])).
% 2.03/2.29 tff(10621,plain,
% 2.03/2.29 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10498, 10620, 7316, 10012, 10615])).
% 2.03/2.29 tff(10622,plain,
% 2.03/2.29 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1432, 10621, 10019])).
% 2.03/2.29 tff(10623,plain,
% 2.03/2.29 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1376, 10622, 8715])).
% 2.03/2.29 tff(10624,plain,
% 2.03/2.29 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1263, 10623, 1])).
% 2.03/2.29 tff(10625,plain,
% 2.03/2.29 (~b(z, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3994, 426, 10613])).
% 2.03/2.29 tff(10626,plain,
% 2.03/2.29 (r(z, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[644, 10625])).
% 2.03/2.29 tff(10627,plain,
% 2.03/2.29 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10613])).
% 2.03/2.29 tff(10628,plain,
% 2.03/2.29 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10627])).
% 2.03/2.29 tff(10629,plain,
% 2.03/2.29 (r(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10622, 10628])).
% 2.03/2.29 tff(10630,plain,
% 2.03/2.29 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3674, 10629, 10626])).
% 2.03/2.29 tff(10631,plain,
% 2.03/2.29 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[420, 10630, 7])).
% 2.03/2.29 tff(10632,plain,
% 2.03/2.29 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[114])).
% 2.03/2.29 tff(10633,plain,
% 2.03/2.29 (b(elem!1, s(s(s(elem!1))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[235, 10632])).
% 2.03/2.29 tff(10634,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1718, 10633])).
% 2.03/2.29 tff(10635,plain,((~b(z, s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10636,plain,
% 2.03/2.29 (~b(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10635, 10617, 10613])).
% 2.03/2.29 tff(10637,plain,
% 2.03/2.29 (r(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[197, 10636])).
% 2.03/2.29 tff(10638,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3360, 10629, 10637])).
% 2.03/2.29 tff(10639,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1239, 10638, 1304])).
% 2.03/2.29 tff(10640,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1295, 10639, 10631, 10620, 10624])).
% 2.03/2.29 tff(10641,plain,(b(elem!1, s(elem!1)) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10642,plain,
% 2.03/2.29 (b(elem!1, s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10641, 1])).
% 2.03/2.29 tff(10643,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10080, 10642, 7316, 10012])).
% 2.03/2.29 tff(10644,plain,
% 2.03/2.29 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1263, 10643, 1])).
% 2.03/2.29 tff(10645,plain,
% 2.03/2.29 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8124, 10616])).
% 2.03/2.29 tff(10646,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2334, 10642, 7316, 10615])).
% 2.03/2.29 tff(10647,plain,
% 2.03/2.29 (r(s(elem!1), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2091, 32, 10646, 10645])).
% 2.03/2.29 tff(10648,plain,
% 2.03/2.29 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3851, 245, 7316, 10615, 10642, 10012])).
% 2.03/2.29 tff(10649,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1239, 10648, 1304])).
% 2.03/2.29 tff(10650,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2357, 10649, 10647, 10644])).
% 2.03/2.29 tff(10651,plain,(s(elem!1) = s(s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10652,plain,
% 2.03/2.29 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.03/2.29 inference(symmetry,[status(thm)],[10651])).
% 2.03/2.29 tff(10653,plain,
% 2.03/2.29 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10652])).
% 2.03/2.29 tff(10654,plain,
% 2.03/2.29 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10653])).
% 2.03/2.29 tff(10655,plain,
% 2.03/2.29 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10651])).
% 2.03/2.29 tff(10656,plain,
% 2.03/2.29 (s(s(s(elem!1))) = elem!1),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3840, 10651])).
% 2.03/2.29 tff(10657,plain,
% 2.03/2.29 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10651])).
% 2.03/2.29 tff(10658,plain,
% 2.03/2.29 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10657])).
% 2.03/2.29 tff(10659,plain,
% 2.03/2.29 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10658])).
% 2.03/2.29 tff(10660,plain,
% 2.03/2.29 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 2.03/2.29 inference(transitivity,[status(thm)],[10659, 10656])).
% 2.03/2.29 tff(10661,plain,
% 2.03/2.29 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10660])).
% 2.03/2.29 tff(10662,plain,
% 2.03/2.29 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(elem!1))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10661, 10651])).
% 2.03/2.29 tff(10663,plain,
% 2.03/2.29 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10662])).
% 2.03/2.29 tff(10664,plain,
% 2.03/2.29 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10663])).
% 2.03/2.29 tff(10665,plain,
% 2.03/2.29 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10664])).
% 2.03/2.29 tff(10666,plain,
% 2.03/2.29 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10651])).
% 2.03/2.29 tff(10667,plain,
% 2.03/2.29 (r(s(elem!1), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[3835])).
% 2.03/2.29 tff(10668,plain,
% 2.03/2.29 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.03/2.29 inference(symmetry,[status(thm)],[10667])).
% 2.03/2.29 tff(10669,plain,
% 2.03/2.29 (r(s(elem!1), elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[130, 10668])).
% 2.03/2.29 tff(10670,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[565, 10669])).
% 2.03/2.29 tff(10671,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | r(s(elem!1), elem!1) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10672,plain,
% 2.03/2.29 (r(s(elem!1), elem!1) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10671, 10651])).
% 2.03/2.29 tff(10673,plain,
% 2.03/2.29 (r(s(elem!1), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10672, 130])).
% 2.03/2.29 tff(10674,plain,
% 2.03/2.29 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(elem!1))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10666])).
% 2.03/2.29 tff(10675,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10656])).
% 2.03/2.29 tff(10676,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10651])).
% 2.03/2.29 tff(10677,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10676, 10675, 10674])).
% 2.03/2.29 tff(10678,plain,
% 2.03/2.29 (b(elem!1, s(elem!1))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[1287, 10677])).
% 2.03/2.30 tff(10679,plain,
% 2.03/2.30 ($false),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[426, 10678])).
% 2.03/2.30 tff(10680,plain,((~b(s(s(s(elem!1))), s(elem!1))) | b(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.30 tff(10681,plain,
% 2.03/2.30 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[10680, 426])).
% 2.03/2.30 tff(10682,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[353, 10681, 11])).
% 2.03/2.30 tff(10683,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), elem!1) <=> r(elem!1, elem!1)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10656])).
% 2.03/2.30 tff(10684,plain,
% 2.03/2.30 (r(elem!1, elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.03/2.30 inference(symmetry,[status(thm)],[10683])).
% 2.03/2.30 tff(10685,plain,
% 2.03/2.30 ((~r(elem!1, elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10684])).
% 2.03/2.30 tff(10686,plain,
% 2.03/2.30 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 2.03/2.30 inference(quant_inst,[status(thm)],[])).
% 2.03/2.30 tff(10687,plain,
% 2.03/2.30 (~r(elem!1, elem!1)),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[10686, 9758])).
% 2.03/2.30 tff(10688,plain,
% 2.03/2.30 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[10687, 10685])).
% 2.03/2.30 tff(10689,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[97])).
% 2.03/2.30 tff(10690,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.30 inference(symmetry,[status(thm)],[10689])).
% 2.03/2.30 tff(10691,plain,
% 2.03/2.30 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10690])).
% 2.03/2.30 tff(10692,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.03/2.30 tff(10693,plain,
% 2.03/2.30 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[10692, 10691])).
% 2.03/2.30 tff(10694,plain,
% 2.03/2.30 ($false),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[371, 10693])).
% 2.03/2.30 tff(10695,plain,((~(s(elem!1) = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.30 tff(10696,plain,
% 2.03/2.30 ((~(s(elem!1) = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[10695, 10688])).
% 2.03/2.30 tff(10697,plain,
% 2.03/2.30 (~(s(elem!1) = elem!1)),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[10696, 10682])).
% 2.03/2.30 tff(10698,plain,
% 2.03/2.30 (~(elem!1 = s(elem!1))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[1074, 10697])).
% 2.03/2.30 tff(10699,plain,
% 2.03/2.30 (r(elem!1, s(elem!1))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[2777, 10698, 426])).
% 2.03/2.30 tff(10700,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10656])).
% 2.03/2.30 tff(10701,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10651])).
% 2.03/2.30 tff(10702,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.30 inference(transitivity,[status(thm)],[10701, 10700])).
% 2.03/2.30 tff(10703,plain,
% 2.03/2.30 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[10682, 10702])).
% 2.03/2.30 tff(10704,plain,
% 2.03/2.30 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10656])).
% 2.03/2.30 tff(10705,plain,
% 2.03/2.30 (r(elem!1, z)),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[1355, 10704])).
% 2.03/2.30 tff(10706,plain,
% 2.03/2.30 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10656])).
% 2.03/2.30 tff(10707,plain,
% 2.03/2.30 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 2.03/2.30 inference(symmetry,[status(thm)],[10706])).
% 2.03/2.30 tff(10708,plain,
% 2.03/2.30 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10651])).
% 2.03/2.30 tff(10709,plain,
% 2.03/2.30 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[8945, 10708])).
% 2.03/2.30 tff(10710,plain,
% 2.03/2.30 (b(s(elem!1), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10651])).
% 2.03/2.30 tff(10711,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 2.03/2.30 tff(10712,plain,
% 2.03/2.30 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10656])).
% 2.03/2.30 tff(10713,plain,
% 2.03/2.30 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10712, 338])).
% 2.13/2.30 tff(10714,plain,
% 2.13/2.30 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10713])).
% 2.13/2.30 tff(10715,plain,
% 2.13/2.30 (~(elem!1 = s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[1128, 10714])).
% 2.13/2.30 tff(10716,plain,
% 2.13/2.30 (b(elem!1, s(z)) | r(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[281, 10715])).
% 2.13/2.30 tff(10717,plain,
% 2.13/2.30 (r(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10716, 10711])).
% 2.13/2.30 tff(10718,plain,
% 2.13/2.30 (~r(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4206, 10717, 572])).
% 2.13/2.30 tff(10719,plain,
% 2.13/2.30 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 2.13/2.30 inference(symmetry,[status(thm)],[343])).
% 2.13/2.30 tff(10720,plain,
% 2.13/2.30 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10652])).
% 2.13/2.30 tff(10721,plain,
% 2.13/2.30 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(elem!1))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10720, 343])).
% 2.13/2.30 tff(10722,plain,
% 2.13/2.30 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10721, 10719])).
% 2.13/2.30 tff(10723,plain,
% 2.13/2.30 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10722])).
% 2.13/2.30 tff(10724,plain,
% 2.13/2.30 (~(s(elem!1) = s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[209, 10723])).
% 2.13/2.30 tff(10725,plain,
% 2.13/2.30 (b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[369, 10724])).
% 2.13/2.30 tff(10726,plain,
% 2.13/2.30 (b(s(elem!1), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10725, 10718])).
% 2.13/2.30 tff(10727,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10726, 10710])).
% 2.13/2.30 tff(10728,plain,
% 2.13/2.30 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[91])).
% 2.13/2.30 tff(10729,plain,
% 2.13/2.30 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10728])).
% 2.13/2.30 tff(10730,plain,
% 2.13/2.30 ((~b(elem!1, s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10729])).
% 2.13/2.30 tff(10731,plain,
% 2.13/2.30 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10711, 10730])).
% 2.13/2.30 tff(10732,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7047, 10731])).
% 2.13/2.30 tff(10733,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10734,plain,
% 2.13/2.30 ((~b(s(s(s(elem!1))), s(z))) | b(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10733, 10656])).
% 2.13/2.30 tff(10735,plain,
% 2.13/2.30 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10734, 10711])).
% 2.13/2.30 tff(10736,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[265, 10735])).
% 2.13/2.30 tff(10737,plain,
% 2.13/2.30 (~r(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1457, 10736, 1355])).
% 2.13/2.30 tff(10738,plain,
% 2.13/2.30 (b(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1421, 10737])).
% 2.13/2.30 tff(10739,plain,
% 2.13/2.30 (~r(s(z), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2177, 10736, 1355])).
% 2.13/2.30 tff(10740,plain,
% 2.13/2.30 (b(s(z), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[232, 10739])).
% 2.13/2.30 tff(10741,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10742,plain,
% 2.13/2.30 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10743,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10742])).
% 2.13/2.30 tff(10744,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10743, 10741])).
% 2.13/2.30 tff(10745,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(10746,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10745, 10744])).
% 2.13/2.30 tff(10747,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10746, 245, 10740, 2197, 10738, 10727])).
% 2.13/2.30 tff(10748,plain,(b(elem!1, s(z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10749,plain,
% 2.13/2.30 (b(elem!1, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10748, 10709, 1355, 10673])).
% 2.13/2.30 tff(10750,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[146, 131, 130])).
% 2.13/2.30 tff(10751,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2558, 10750])).
% 2.13/2.30 tff(10752,plain,
% 2.13/2.30 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[9644, 245, 2197, 10751, 6811])).
% 2.13/2.30 tff(10753,plain,
% 2.13/2.30 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10752, 10665])).
% 2.13/2.30 tff(10754,plain,
% 2.13/2.30 (((~![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(z))))), elem!1)) | (~r(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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10755,plain,
% 2.13/2.30 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(10756,plain,
% 2.13/2.30 ((~![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(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10755, 10754])).
% 2.13/2.30 tff(10757,plain,
% 2.13/2.30 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10756, 141, 130, 2628])).
% 2.13/2.30 tff(10758,plain,
% 2.13/2.30 (s(s(s(elem!1))) = elem!1),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3840, 3835])).
% 2.13/2.30 tff(10759,plain,
% 2.13/2.30 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[3835])).
% 2.13/2.30 tff(10760,plain,
% 2.13/2.30 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10759])).
% 2.13/2.30 tff(10761,plain,
% 2.13/2.30 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10760])).
% 2.13/2.30 tff(10762,plain,
% 2.13/2.30 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 2.13/2.30 inference(transitivity,[status(thm)],[10761, 10758])).
% 2.13/2.30 tff(10763,plain,
% 2.13/2.30 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10762])).
% 2.13/2.30 tff(10764,plain,
% 2.13/2.30 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10763])).
% 2.13/2.30 tff(10765,plain,
% 2.13/2.30 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.13/2.30 inference(symmetry,[status(thm)],[3835])).
% 2.13/2.30 tff(10766,plain,
% 2.13/2.30 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10765, 10764])).
% 2.13/2.30 tff(10767,plain,
% 2.13/2.30 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10766])).
% 2.13/2.30 tff(10768,plain,
% 2.13/2.30 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10767])).
% 2.13/2.30 tff(10769,plain,
% 2.13/2.30 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[6955, 10768])).
% 2.13/2.30 tff(10770,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.13/2.30 tff(10771,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10770, 10769])).
% 2.13/2.30 tff(10772,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10773,plain,
% 2.13/2.30 ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10772, 10651])).
% 2.13/2.30 tff(10774,plain,
% 2.13/2.30 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10773, 10757])).
% 2.13/2.30 tff(10775,plain,
% 2.13/2.30 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[599, 10763, 3835])).
% 2.13/2.30 tff(10776,plain,
% 2.13/2.30 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10775])).
% 2.13/2.30 tff(10777,plain,
% 2.13/2.30 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[604, 10776, 113])).
% 2.13/2.30 tff(10778,plain,
% 2.13/2.30 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10777])).
% 2.13/2.30 tff(10779,plain,
% 2.13/2.30 (s(s(s(z))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[1043, 10778, 157, 10759])).
% 2.13/2.30 tff(10780,plain,
% 2.13/2.30 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10779])).
% 2.13/2.30 tff(10781,plain,
% 2.13/2.30 (s(s(z)) = s(s(s(s(elem!1))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[586, 10780, 318])).
% 2.13/2.30 tff(10782,plain,
% 2.13/2.30 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10781])).
% 2.13/2.30 tff(10783,plain,
% 2.13/2.30 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10782])).
% 2.13/2.30 tff(10784,plain,
% 2.13/2.30 (elem!1 = s(s(s(elem!1)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10758])).
% 2.13/2.30 tff(10785,plain,
% 2.13/2.30 (elem!1 = s(z)),
% 2.13/2.30 inference(transitivity,[status(thm)],[10784, 206, 10783, 590])).
% 2.13/2.30 tff(10786,plain,
% 2.13/2.30 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10758])).
% 2.13/2.30 tff(10787,plain,
% 2.13/2.30 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10786, 338])).
% 2.13/2.30 tff(10788,plain,
% 2.13/2.30 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10787])).
% 2.13/2.30 tff(10789,plain,
% 2.13/2.30 (~(elem!1 = s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[1128, 10788])).
% 2.13/2.30 tff(10790,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10789, 10785])).
% 2.13/2.30 tff(10791,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10792,plain,
% 2.13/2.30 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10791, 10651])).
% 2.13/2.30 tff(10793,plain,
% 2.13/2.30 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[797, 10792])).
% 2.13/2.30 tff(10794,plain,
% 2.13/2.30 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10793, 10774])).
% 2.13/2.30 tff(10795,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10794, 10753])).
% 2.13/2.30 tff(10796,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10797,plain,
% 2.13/2.30 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10796, 10709, 130, 131])).
% 2.13/2.30 tff(10798,plain,
% 2.13/2.30 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[678, 10784])).
% 2.13/2.30 tff(10799,plain,
% 2.13/2.30 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10798])).
% 2.13/2.30 tff(10800,plain,
% 2.13/2.30 (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[604, 10799, 157, 10759])).
% 2.13/2.30 tff(10801,plain,
% 2.13/2.30 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10800])).
% 2.13/2.30 tff(10802,plain,
% 2.13/2.30 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(z)))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10801])).
% 2.13/2.30 tff(10803,plain,
% 2.13/2.30 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[1485, 10802, 597])).
% 2.13/2.30 tff(10804,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 2.13/2.30 tff(10805,plain,
% 2.13/2.30 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10804])).
% 2.13/2.30 tff(10806,plain,
% 2.13/2.30 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10805])).
% 2.13/2.30 tff(10807,plain,
% 2.13/2.30 (s(s(z)) = s(s(s(elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[586, 10806, 113])).
% 2.13/2.30 tff(10808,plain,
% 2.13/2.30 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10807])).
% 2.13/2.30 tff(10809,plain,
% 2.13/2.30 (s(z) = s(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[591, 10808, 157, 10759])).
% 2.13/2.30 tff(10810,plain,
% 2.13/2.30 (inj_0(s(z)) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10809])).
% 2.13/2.30 tff(10811,plain,
% 2.13/2.30 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10810])).
% 2.13/2.30 tff(10812,plain,
% 2.13/2.30 (s(s(s(s(elem!1)))) = z),
% 2.13/2.30 inference(transitivity,[status(thm)],[1485, 10811, 52])).
% 2.13/2.30 tff(10813,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[66, 10812])).
% 2.13/2.30 tff(10814,plain,((~(s(s(s(s(elem!1)))) = s(s(s(z))))) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10815,plain,
% 2.13/2.30 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10814, 3835])).
% 2.13/2.30 tff(10816,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10815, 10803])).
% 2.13/2.30 tff(10817,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10818,plain,
% 2.13/2.30 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10817, 10651])).
% 2.13/2.30 tff(10819,plain,
% 2.13/2.30 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[775, 10818])).
% 2.13/2.30 tff(10820,plain,
% 2.13/2.30 (b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[787, 10819])).
% 2.13/2.30 tff(10821,plain,
% 2.13/2.30 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10820, 10797])).
% 2.13/2.30 tff(10822,plain,
% 2.13/2.30 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10814, 10651])).
% 2.13/2.30 tff(10823,plain,
% 2.13/2.30 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[830, 141, 289])).
% 2.13/2.30 tff(10824,plain,
% 2.13/2.30 (~r(s(s(s(z))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10823, 816])).
% 2.13/2.30 tff(10825,plain,
% 2.13/2.30 (b(s(s(s(z))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[836, 32, 833, 10824])).
% 2.13/2.30 tff(10826,plain,
% 2.13/2.30 (((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10827,plain,
% 2.13/2.30 ((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(10828,plain,
% 2.13/2.30 ((~![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(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10827, 10826])).
% 2.13/2.30 tff(10829,plain,
% 2.13/2.30 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10828, 141, 130])).
% 2.13/2.30 tff(10830,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10829, 816])).
% 2.13/2.30 tff(10831,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10261, 32, 10257, 10830])).
% 2.13/2.30 tff(10832,plain,
% 2.13/2.30 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1980, 141, 289, 130])).
% 2.13/2.30 tff(10833,plain,
% 2.13/2.30 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1992, 10832])).
% 2.13/2.30 tff(10834,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10835,plain,
% 2.13/2.30 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10836,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10835])).
% 2.13/2.30 tff(10837,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10836, 10834])).
% 2.13/2.30 tff(10838,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(10839,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10838, 10837])).
% 2.13/2.30 tff(10840,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10839, 245, 10833, 1943, 10831, 10825])).
% 2.13/2.30 tff(10841,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10842,plain,
% 2.13/2.30 ((~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10841, 10822])).
% 2.13/2.30 tff(10843,plain,
% 2.13/2.30 (~r(s(s(s(z))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10842, 289, 130, 1943])).
% 2.13/2.30 tff(10844,plain,
% 2.13/2.30 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10660])).
% 2.13/2.30 tff(10845,plain,
% 2.13/2.30 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(z))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10844, 686])).
% 2.13/2.30 tff(10846,plain,
% 2.13/2.30 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = elem!1)),
% 2.13/2.30 inference(transitivity,[status(thm)],[10845, 10151])).
% 2.13/2.30 tff(10847,plain,
% 2.13/2.30 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10846])).
% 2.13/2.30 tff(10848,assumption,(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.13/2.30 tff(10849,plain,
% 2.13/2.30 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10848, 10761])).
% 2.13/2.30 tff(10850,plain,
% 2.13/2.30 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10849])).
% 2.13/2.30 tff(10851,plain,
% 2.13/2.30 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[586, 10850, 157, 10759])).
% 2.13/2.30 tff(10852,plain,
% 2.13/2.30 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10851])).
% 2.13/2.30 tff(10853,plain,
% 2.13/2.30 (s(z) = s(elem!1)),
% 2.13/2.30 inference(transitivity,[status(thm)],[591, 10852, 318, 10765])).
% 2.13/2.30 tff(10854,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10758])).
% 2.13/2.30 tff(10855,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 2.13/2.30 inference(transitivity,[status(thm)],[10854, 119])).
% 2.13/2.30 tff(10856,plain,
% 2.13/2.30 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10855])).
% 2.13/2.30 tff(10857,plain,
% 2.13/2.30 (~(z = elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[22, 10856])).
% 2.13/2.30 tff(10858,plain,
% 2.13/2.30 (~(s(z) = s(elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[57, 10857])).
% 2.13/2.30 tff(10859,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10858, 10853])).
% 2.13/2.30 tff(10860,plain,((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10861,plain,
% 2.13/2.30 (~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10860, 10651])).
% 2.13/2.30 tff(10862,plain,
% 2.13/2.30 (~(s(s(s(z))) = elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10861, 10847])).
% 2.13/2.30 tff(10863,plain,
% 2.13/2.30 (b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7257, 10862])).
% 2.13/2.30 tff(10864,plain,
% 2.13/2.30 (b(s(s(s(z))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10863, 10843])).
% 2.13/2.30 tff(10865,plain,
% 2.13/2.30 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10721])).
% 2.13/2.30 tff(10866,plain,
% 2.13/2.30 (~(s(z) = s(elem!1))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[209, 10865])).
% 2.13/2.30 tff(10867,plain,
% 2.13/2.30 ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[670, 10866])).
% 2.13/2.30 tff(10868,plain,
% 2.13/2.30 (~r(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10867, 289, 10673])).
% 2.13/2.30 tff(10869,plain,
% 2.13/2.30 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.13/2.30 inference(transitivity,[status(thm)],[10713, 339])).
% 2.13/2.30 tff(10870,plain,
% 2.13/2.30 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10869])).
% 2.13/2.30 tff(10871,plain,
% 2.13/2.30 (~(s(z) = elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[1128, 10870])).
% 2.13/2.30 tff(10872,plain,
% 2.13/2.30 (b(s(z), elem!1) | r(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[389, 10871])).
% 2.13/2.30 tff(10873,plain,
% 2.13/2.30 (b(s(z), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10872, 10868])).
% 2.13/2.30 tff(10874,plain,
% 2.13/2.30 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 2.13/2.30 inference(commutativity,[status(thm)],[])).
% 2.13/2.30 tff(10875,plain,
% 2.13/2.30 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10874])).
% 2.13/2.30 tff(10876,plain,
% 2.13/2.30 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10875])).
% 2.13/2.30 tff(10877,plain,
% 2.13/2.30 (~(s(z) = s(s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[892, 10876])).
% 2.13/2.30 tff(10878,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), 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(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10879,plain,
% 2.13/2.31 (((~b(s(z), elem!1)) | (~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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10880,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10879])).
% 2.13/2.31 tff(10881,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10880, 10878])).
% 2.13/2.31 tff(10882,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10883,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10882, 10881])).
% 2.13/2.31 tff(10884,plain,
% 2.13/2.31 (~b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10883, 245, 301, 447, 954])).
% 2.13/2.31 tff(10885,plain,
% 2.13/2.31 (((~![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)))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10886,plain,
% 2.13/2.31 ((~![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)))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10887,plain,
% 2.13/2.31 ((~![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))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10886, 10885])).
% 2.13/2.31 tff(10888,plain,
% 2.13/2.31 ((s(z) = s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10887, 32, 10884])).
% 2.13/2.31 tff(10889,plain,
% 2.13/2.31 (r(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10888, 10877])).
% 2.13/2.31 tff(10890,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~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(X0, 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))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10891,plain,
% 2.13/2.31 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10892,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10891])).
% 2.13/2.31 tff(10893,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10892, 10890])).
% 2.13/2.31 tff(10894,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10895,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10894, 10893])).
% 2.13/2.31 tff(10896,plain,
% 2.13/2.31 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10895, 245, 301, 447, 4878, 954])).
% 2.13/2.31 tff(10897,plain,
% 2.13/2.31 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1515, 10896])).
% 2.13/2.31 tff(10898,plain,
% 2.13/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10899,plain,
% 2.13/2.31 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10900,plain,
% 2.13/2.31 (((~![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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10899])).
% 2.13/2.31 tff(10901,plain,
% 2.13/2.31 (((~![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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10900, 10898])).
% 2.13/2.31 tff(10902,plain,
% 2.13/2.31 ((~![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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10903,plain,
% 2.13/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10902, 10901])).
% 2.13/2.31 tff(10904,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10903, 141, 6827, 10897, 10889])).
% 2.13/2.31 tff(10905,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10906,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10905, 10873, 10864, 4878, 301])).
% 2.13/2.31 tff(10907,plain,((~r(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10908,plain,
% 2.13/2.31 (~r(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10907, 10821, 10749, 130, 10751])).
% 2.13/2.31 tff(10909,plain,
% 2.13/2.31 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10656])).
% 2.13/2.31 tff(10910,plain,
% 2.13/2.31 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 2.13/2.31 inference(transitivity,[status(thm)],[10909, 119])).
% 2.13/2.31 tff(10911,plain,
% 2.13/2.31 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10910])).
% 2.13/2.31 tff(10912,plain,
% 2.13/2.31 (~(z = elem!1)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[22, 10911])).
% 2.13/2.31 tff(10913,plain,
% 2.13/2.31 (b(z, elem!1) | r(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[175, 10912])).
% 2.13/2.31 tff(10914,plain,
% 2.13/2.31 (b(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10913, 10908])).
% 2.13/2.31 tff(10915,plain,
% 2.13/2.31 (~b(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6835, 10914, 10821, 10749])).
% 2.13/2.31 tff(10916,plain,
% 2.13/2.31 (r(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10872, 10915])).
% 2.13/2.31 tff(10917,plain,
% 2.13/2.31 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10916, 10707])).
% 2.13/2.31 tff(10918,plain,
% 2.13/2.31 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10765])).
% 2.13/2.31 tff(10919,plain,
% 2.13/2.31 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(symmetry,[status(thm)],[10918])).
% 2.13/2.31 tff(10920,plain,
% 2.13/2.31 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[486, 10919])).
% 2.13/2.31 tff(10921,plain,
% 2.13/2.31 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2458, 141, 1368, 619])).
% 2.13/2.31 tff(10922,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10921, 10920])).
% 2.13/2.31 tff(10923,plain,((~r(s(z), s(elem!1))) | (~(s(elem!1) = s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10924,plain,
% 2.13/2.31 ((~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10923, 10651])).
% 2.13/2.31 tff(10925,plain,
% 2.13/2.31 (~r(s(z), s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10924, 10916, 1368])).
% 2.13/2.31 tff(10926,plain,
% 2.13/2.31 (b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[440, 10866])).
% 2.13/2.31 tff(10927,plain,
% 2.13/2.31 (b(s(z), s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10926, 10925])).
% 2.13/2.31 tff(10928,plain,
% 2.13/2.31 (~b(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2291, 10927, 10709, 10020, 10751])).
% 2.13/2.31 tff(10929,plain,
% 2.13/2.31 (r(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[232, 10928])).
% 2.13/2.31 tff(10930,plain,
% 2.13/2.31 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2109, 10929, 1355])).
% 2.13/2.31 tff(10931,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10930, 10917])).
% 2.13/2.31 tff(10932,plain,((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10933,plain,
% 2.13/2.31 (~r(elem!1, z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10932, 1355, 1368, 130, 1367])).
% 2.13/2.31 tff(10934,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10933, 10705])).
% 2.13/2.31 tff(10935,plain,((~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10936,plain,
% 2.13/2.31 (~r(s(s(s(elem!1))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10935, 10703, 130, 10699])).
% 2.13/2.31 tff(10937,plain,
% 2.13/2.31 (b(s(s(s(elem!1))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[37, 10936])).
% 2.13/2.31 tff(10938,plain,
% 2.13/2.31 ((~r(s(s(s(elem!1))), z)) <=> (~r(elem!1, z))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10704])).
% 2.13/2.31 tff(10939,plain,
% 2.13/2.31 (~r(elem!1, z)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10936, 10938])).
% 2.13/2.31 tff(10940,plain,
% 2.13/2.31 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 2.13/2.31 inference(transitivity,[status(thm)],[10910, 3639])).
% 2.13/2.31 tff(10941,plain,
% 2.13/2.31 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10940])).
% 2.13/2.31 tff(10942,plain,
% 2.13/2.31 (~(elem!1 = z)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[22, 10941])).
% 2.13/2.31 tff(10943,plain,
% 2.13/2.31 (b(elem!1, z) | r(elem!1, z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[128, 10942])).
% 2.13/2.31 tff(10944,plain,
% 2.13/2.31 (b(elem!1, z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10943, 10939])).
% 2.13/2.31 tff(10945,plain,
% 2.13/2.31 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10652])).
% 2.13/2.31 tff(10946,plain,
% 2.13/2.31 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(symmetry,[status(thm)],[10945])).
% 2.13/2.31 tff(10947,plain,
% 2.13/2.31 (r(s(elem!1), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[3835])).
% 2.13/2.31 tff(10948,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), z) <=> r(s(elem!1), z)),
% 2.13/2.31 inference(symmetry,[status(thm)],[10947])).
% 2.13/2.31 tff(10949,plain,
% 2.13/2.31 (r(s(elem!1), z)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[106, 10948])).
% 2.13/2.31 tff(10950,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1037, 10949])).
% 2.13/2.31 tff(10951,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | r(s(elem!1), z) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10952,plain,
% 2.13/2.31 (r(s(elem!1), z) | (~r(s(s(s(s(elem!1)))), z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10951, 10651])).
% 2.13/2.31 tff(10953,plain,
% 2.13/2.31 (r(s(elem!1), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10952, 106])).
% 2.13/2.31 tff(10954,plain,
% 2.13/2.31 (~r(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[649, 10953, 10673])).
% 2.13/2.31 tff(10955,plain,
% 2.13/2.31 (b(z, elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10913, 10954])).
% 2.13/2.31 tff(10956,plain,
% 2.13/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10957,plain,
% 2.13/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10958,plain,
% 2.13/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10957, 10956])).
% 2.13/2.31 tff(10959,plain,
% 2.13/2.31 ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10958, 141, 310])).
% 2.13/2.31 tff(10960,plain,
% 2.13/2.31 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10959, 8433])).
% 2.13/2.31 tff(10961,plain,
% 2.13/2.31 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[738, 10960])).
% 2.13/2.31 tff(10962,plain,
% 2.13/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10963,plain,
% 2.13/2.31 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10964,plain,
% 2.13/2.31 (((~![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(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10963])).
% 2.13/2.31 tff(10965,plain,
% 2.13/2.31 (((~![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(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10964, 10962])).
% 2.13/2.31 tff(10966,plain,
% 2.13/2.31 ((~![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(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10967,plain,
% 2.13/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10966, 10965])).
% 2.13/2.31 tff(10968,plain,
% 2.13/2.31 ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10967, 141, 1368])).
% 2.13/2.31 tff(10969,plain,
% 2.13/2.31 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10968, 8433])).
% 2.13/2.31 tff(10970,plain,
% 2.13/2.31 (b(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[720, 10969, 773])).
% 2.13/2.31 tff(10971,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10972,plain,
% 2.13/2.31 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10973,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10972])).
% 2.13/2.31 tff(10974,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10973, 10971])).
% 2.13/2.31 tff(10975,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10976,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10975, 10974])).
% 2.13/2.31 tff(10977,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10976, 245, 4105, 4186, 10970, 10961])).
% 2.13/2.31 tff(10978,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (elem!1 = s(s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10979,plain,
% 2.13/2.31 ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10978, 10818])).
% 2.13/2.31 tff(10980,plain,
% 2.13/2.31 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10979, 310, 1368, 4186, 10955])).
% 2.13/2.31 tff(10981,plain,
% 2.13/2.31 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10773, 10980])).
% 2.13/2.31 tff(10982,plain,
% 2.13/2.31 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10793, 10981])).
% 2.13/2.31 tff(10983,plain,
% 2.13/2.31 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10982, 10663])).
% 2.13/2.31 tff(10984,plain,
% 2.13/2.31 (~r(s(z), s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10924, 619, 1368])).
% 2.13/2.31 tff(10985,plain,
% 2.13/2.31 (b(s(z), s(elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10926, 10984])).
% 2.13/2.31 tff(10986,plain,
% 2.13/2.31 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10987,plain,
% 2.13/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10988,plain,
% 2.13/2.31 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10987, 10986])).
% 2.13/2.31 tff(10989,plain,
% 2.13/2.31 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10988, 141, 619, 130])).
% 2.13/2.31 tff(10990,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(elem!1), s(z))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10765])).
% 2.13/2.31 tff(10991,plain,
% 2.13/2.31 (r(s(elem!1), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.31 inference(symmetry,[status(thm)],[10990])).
% 2.13/2.31 tff(10992,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[998, 10991])).
% 2.13/2.31 tff(10993,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[212, 10992])).
% 2.13/2.31 tff(10994,plain,(r(s(s(s(s(elem!1)))), s(z)) | (~r(s(elem!1), s(z))) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10995,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(z)) | (~r(s(elem!1), s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10994, 10651])).
% 2.13/2.31 tff(10996,plain,
% 2.13/2.31 (~r(s(elem!1), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10995, 10989])).
% 2.13/2.31 tff(10997,plain,
% 2.13/2.31 (b(s(elem!1), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10725, 10996])).
% 2.13/2.31 tff(10998,plain,
% 2.13/2.31 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10661])).
% 2.13/2.31 tff(10999,plain,
% 2.13/2.31 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10998, 9086])).
% 2.13/2.31 tff(11000,plain,
% 2.13/2.31 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.31 tff(11001,plain,
% 2.13/2.31 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10792, 11000])).
% 2.13/2.31 tff(11002,plain,
% 2.13/2.31 ((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6906, 11001])).
% 2.13/2.31 tff(11003,plain,
% 2.13/2.31 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[11002, 10997, 619, 10673, 10985])).
% 2.13/2.31 tff(11004,plain,
% 2.13/2.31 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10820, 11003])).
% 2.13/2.31 tff(11005,plain,
% 2.13/2.31 (~b(z, s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6989, 245, 10955, 4186, 11004])).
% 2.13/2.31 tff(11006,plain,
% 2.13/2.31 (r(z, s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[758, 11005])).
% 2.13/2.31 tff(11007,plain,
% 2.13/2.31 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10661])).
% 2.13/2.31 tff(11008,plain,
% 2.13/2.31 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10661])).
% 2.13/2.31 tff(11009,plain,
% 2.13/2.31 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(symmetry,[status(thm)],[11008])).
% 2.13/2.31 tff(11010,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10652])).
% 2.13/2.31 tff(11011,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[11010, 11009])).
% 2.13/2.31 tff(11012,plain,
% 2.13/2.31 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[11011])).
% 2.13/2.31 tff(11013,plain,
% 2.13/2.31 (~b(s(s(s(s(s(z))))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6914, 245, 10955, 4186, 11004])).
% 2.13/2.31 tff(11014,plain,
% 2.13/2.31 (r(s(s(s(s(s(z))))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[738, 11013])).
% 2.13/2.31 tff(11015,plain,
% 2.13/2.31 (((~![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(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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11016,plain,
% 2.13/2.32 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11017,plain,
% 2.13/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11016])).
% 2.13/2.32 tff(11018,plain,
% 2.13/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[11017, 11015])).
% 2.13/2.32 tff(11019,plain,
% 2.13/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(11020,plain,
% 2.13/2.32 ((~![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(z))))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11019, 11018])).
% 2.13/2.32 tff(11021,plain,
% 2.13/2.32 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11020, 141, 106, 11014])).
% 2.13/2.32 tff(11022,plain,
% 2.13/2.32 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11021, 11012])).
% 2.13/2.32 tff(11023,plain,
% 2.13/2.32 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8176, 10792])).
% 2.13/2.32 tff(11024,plain,
% 2.13/2.32 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6009, 11023])).
% 2.13/2.32 tff(11025,plain,
% 2.13/2.32 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11024, 11022])).
% 2.13/2.32 tff(11026,plain,
% 2.13/2.32 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11025, 11007])).
% 2.13/2.32 tff(11027,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11026, 10654])).
% 2.13/2.32 tff(11028,plain,
% 2.13/2.32 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10985, 10655])).
% 2.13/2.32 tff(11029,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[217, 10989])).
% 2.13/2.32 tff(11030,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11031,plain,
% 2.13/2.32 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11032,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11031])).
% 2.13/2.32 tff(11033,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[11032, 11030])).
% 2.13/2.32 tff(11034,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(11035,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11034, 11033])).
% 2.13/2.32 tff(11036,plain,
% 2.13/2.32 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11035, 245, 11029, 11028, 8808])).
% 2.13/2.32 tff(11037,plain,
% 2.13/2.32 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[809, 11036])).
% 2.13/2.32 tff(11038,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11039,plain,
% 2.13/2.32 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11040,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11039])).
% 2.13/2.32 tff(11041,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[11040, 11038])).
% 2.13/2.32 tff(11042,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(11043,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11042, 11041])).
% 2.13/2.32 tff(11044,plain,
% 2.13/2.32 (~b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11043, 245, 11029, 11028, 8808])).
% 2.13/2.32 tff(11045,plain,
% 2.13/2.32 (r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1698, 11044])).
% 2.13/2.32 tff(11046,plain,
% 2.13/2.32 (~r(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7006, 141, 11045, 11006])).
% 2.13/2.32 tff(11047,plain,
% 2.13/2.32 (b(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[232, 11046])).
% 2.13/2.32 tff(11048,plain,
% 2.13/2.32 (~b(elem!1, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4214, 245, 10955, 4186, 11047])).
% 2.13/2.32 tff(11049,plain,
% 2.13/2.32 (r(elem!1, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10716, 11048])).
% 2.13/2.32 tff(11050,plain,
% 2.13/2.32 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6045, 141, 11049, 11037])).
% 2.13/2.32 tff(11051,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[720, 10818])).
% 2.13/2.32 tff(11052,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11051, 11050])).
% 2.13/2.32 tff(11053,plain,
% 2.13/2.32 (~r(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6833, 141, 11045, 11006])).
% 2.13/2.32 tff(11054,plain,
% 2.13/2.32 (b(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1421, 11053])).
% 2.13/2.32 tff(11055,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.13/2.32 tff(11056,plain,
% 2.13/2.32 (~r(s(elem!1), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7260, 816, 572])).
% 2.13/2.32 tff(11057,plain,
% 2.13/2.32 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.32 tff(11058,plain,
% 2.13/2.32 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(z))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[11057])).
% 2.13/2.32 tff(11059,plain,
% 2.13/2.32 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11058])).
% 2.13/2.32 tff(11060,plain,
% 2.13/2.32 (~(s(elem!1) = s(s(s(z))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10822, 11059])).
% 2.13/2.32 tff(11061,plain,
% 2.13/2.32 (r(s(elem!1), s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8469, 11060])).
% 2.13/2.32 tff(11062,plain,
% 2.13/2.32 (b(s(elem!1), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11061, 11056])).
% 2.13/2.32 tff(11063,plain,
% 2.13/2.32 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.32 tff(11064,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[11063])).
% 2.13/2.32 tff(11065,plain,
% 2.13/2.32 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(z)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11064])).
% 2.13/2.32 tff(11066,plain,
% 2.13/2.32 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10258, 11065])).
% 2.13/2.32 tff(11067,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8456, 11066])).
% 2.13/2.32 tff(11068,plain,(b(s(s(s(s(elem!1)))), s(s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(11069,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11068, 11062])).
% 2.13/2.32 tff(11070,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 2.13/2.32 tff(11071,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11072,plain,
% 2.13/2.32 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11073,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11072])).
% 2.13/2.32 tff(11074,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[11073, 11071])).
% 2.13/2.32 tff(11075,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(11076,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11075, 11074])).
% 2.13/2.32 tff(11077,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11076, 245, 11070, 5823, 4878, 6123, 11055])).
% 2.13/2.32 tff(11078,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(11079,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11078, 11069, 5823, 4878, 11055])).
% 2.13/2.32 tff(11080,plain,
% 2.13/2.32 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1515, 11079])).
% 2.13/2.32 tff(11081,plain,
% 2.13/2.32 (~r(s(s(s(z))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7090, 11080, 740])).
% 2.13/2.32 tff(11082,plain,
% 2.13/2.32 (b(s(s(s(z))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7060, 11081])).
% 2.13/2.32 tff(11083,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8573, 11082, 4187, 355])).
% 2.13/2.32 tff(11084,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[895, 32, 8431, 892, 11083])).
% 2.13/2.32 tff(11085,plain,((~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(11086,plain,
% 2.13/2.32 (~r(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11085, 11054, 11047, 11006, 11052, 11004, 11027, 10673, 619])).
% 2.13/2.32 tff(11087,plain,
% 2.13/2.32 (b(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10863, 11086])).
% 2.13/2.32 tff(11088,plain,
% 2.13/2.32 (~b(s(s(s(z))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7251, 245, 10955, 4186, 11087])).
% 2.13/2.32 tff(11089,plain,
% 2.13/2.32 (r(s(s(s(z))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7060, 11088])).
% 2.13/2.32 tff(11090,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), elem!1)) | (~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(X0, 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))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11091,plain,
% 2.13/2.32 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11092,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11091])).
% 2.13/2.32 tff(11093,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[11092, 11090])).
% 2.13/2.32 tff(11094,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(11095,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11094, 11093])).
% 2.13/2.32 tff(11096,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11095, 245, 10955, 4186, 11004, 11087])).
% 2.13/2.32 tff(11097,plain,
% 2.13/2.32 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1515, 11096])).
% 2.13/2.32 tff(11098,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7090, 11097, 11089, 11006])).
% 2.13/2.32 tff(11099,plain,((~r(s(z), elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(11100,plain,
% 2.13/2.32 (~r(s(z), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11099, 10983, 106, 4186, 130, 1368])).
% 2.13/2.32 tff(11101,plain,
% 2.13/2.32 (b(s(z), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10872, 11100])).
% 2.13/2.32 tff(11102,plain,
% 2.13/2.32 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.32 tff(11103,plain,
% 2.13/2.32 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.32 inference(symmetry,[status(thm)],[11102])).
% 2.13/2.32 tff(11104,plain,
% 2.13/2.32 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10663, 11103])).
% 2.13/2.32 tff(11105,plain,
% 2.13/2.32 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10982, 11104])).
% 2.13/2.32 tff(11106,plain,
% 2.13/2.32 (~b(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4436, 11101, 4186, 10955])).
% 2.13/2.32 tff(11107,plain,
% 2.13/2.32 (r(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[232, 11106])).
% 2.13/2.32 tff(11108,plain,
% 2.13/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11109,plain,
% 2.13/2.32 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11110,plain,
% 2.13/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11109])).
% 2.13/2.32 tff(11111,plain,
% 2.13/2.32 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[11110, 11108])).
% 2.13/2.32 tff(11112,plain,
% 2.13/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(11113,plain,
% 2.13/2.32 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11112, 11111])).
% 2.13/2.32 tff(11114,plain,
% 2.13/2.32 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11113, 141, 220, 310])).
% 2.13/2.32 tff(11115,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11114, 10920])).
% 2.13/2.32 tff(11116,plain,((~r(s(z), s(elem!1))) | (~(s(elem!1) = s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(11117,plain,
% 2.13/2.32 ((~r(s(z), s(elem!1))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11116, 10651])).
% 2.13/2.32 tff(11118,plain,
% 2.13/2.32 (~r(s(z), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[11117, 11107, 310])).
% 2.13/2.32 tff(11119,plain,
% 2.13/2.32 (b(s(z), s(elem!1))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10926, 11118])).
% 2.13/2.32 tff(11120,plain,
% 2.13/2.32 (r(z, s(elem!1)) <=> r(z, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.32 tff(11121,plain,
% 2.13/2.32 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(elem!1))),
% 2.13/2.32 inference(symmetry,[status(thm)],[11120])).
% 2.13/2.32 tff(11122,plain,
% 2.13/2.32 (r(z, s(elem!1))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[310, 11121])).
% 2.13/2.32 tff(11123,plain,
% 2.13/2.32 (~b(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4595, 11101, 4186, 10955])).
% 2.13/2.32 tff(11124,plain,
% 2.13/2.32 (r(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1421, 11123])).
% 2.13/2.32 tff(11125,plain,
% 2.13/2.32 (~r(s(elem!1), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4743, 11124, 11122])).
% 2.13/2.32 tff(11126,plain,
% 2.13/2.32 (b(s(elem!1), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10725, 11125])).
% 2.13/2.32 tff(11127,plain,
% 2.13/2.32 (((~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(11128,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[11127])).
% 2.13/2.32 tff(11129,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[11128, 8395])).
% 2.13/2.32 tff(11130,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(11131,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11130, 11129])).
% 2.13/2.33 tff(11132,plain,
% 2.13/2.33 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11131, 245, 655, 4188, 4300])).
% 2.13/2.33 tff(11133,plain,
% 2.13/2.33 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[809, 11132])).
% 2.13/2.33 tff(11134,plain,
% 2.13/2.33 (((~![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(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(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11135,plain,
% 2.13/2.33 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11136,plain,
% 2.13/2.33 (((~![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(z, 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(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[11135])).
% 2.13/2.33 tff(11137,plain,
% 2.13/2.33 (((~![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(z, 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(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[11136, 11134])).
% 2.13/2.33 tff(11138,plain,
% 2.13/2.33 ((~![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(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(11139,plain,
% 2.13/2.33 ((~![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(z, s(s(s(s(s(z)))))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11138, 11137])).
% 2.13/2.33 tff(11140,plain,
% 2.13/2.33 (~r(z, s(s(s(s(s(z))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11139, 141, 7282, 11133])).
% 2.13/2.33 tff(11141,plain,
% 2.13/2.33 (b(z, s(s(s(s(s(z))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[758, 11140])).
% 2.13/2.33 tff(11142,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11143,plain,
% 2.13/2.33 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11144,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[11143])).
% 2.13/2.33 tff(11145,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[11144, 11142])).
% 2.13/2.33 tff(11146,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(11147,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11146, 11145])).
% 2.13/2.33 tff(11148,plain,
% 2.13/2.33 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11147, 245, 655, 4188, 7234])).
% 2.13/2.33 tff(11149,plain,
% 2.13/2.33 (~b(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7242, 7233, 4186, 447, 4105])).
% 2.13/2.33 tff(11150,plain,
% 2.13/2.33 (r(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6065, 32, 11149, 6213])).
% 2.13/2.33 tff(11151,plain,
% 2.13/2.33 (~r(s(elem!1), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[822, 141, 572, 11150])).
% 2.13/2.33 tff(11152,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[826, 32, 610, 11151, 11148])).
% 2.13/2.33 tff(11153,plain,(r(s(s(s(z))), s(z)) | (s(elem!1) = s(s(s(z)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(11154,plain,
% 2.13/2.33 (r(s(s(s(z))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11153, 655, 610, 4188, 572, 6213, 4186, 447, 4105])).
% 2.13/2.33 tff(11155,plain,
% 2.13/2.33 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[899, 141, 11154, 11133])).
% 2.13/2.33 tff(11156,plain,
% 2.13/2.33 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[909, 11155])).
% 2.13/2.33 tff(11157,plain,
% 2.13/2.33 (((~![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))))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11158,plain,
% 2.13/2.33 (((~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))))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11159,plain,
% 2.13/2.33 (((~![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)))))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[11158])).
% 2.13/2.33 tff(11160,plain,
% 2.13/2.33 (((~![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))))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[11159, 11157])).
% 2.13/2.33 tff(11161,plain,
% 2.13/2.33 ((~![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))))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(11162,plain,
% 2.13/2.33 ((~![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)))))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11161, 11160])).
% 2.13/2.33 tff(11163,plain,
% 2.13/2.33 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11162, 141, 11154, 11133])).
% 2.13/2.33 tff(11164,plain,
% 2.13/2.33 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1515, 11163])).
% 2.13/2.33 tff(11165,plain,
% 2.13/2.33 (~r(s(s(s(z))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[985, 11154, 7232])).
% 2.13/2.33 tff(11166,plain,
% 2.13/2.33 (b(s(s(s(z))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7060, 11165])).
% 2.13/2.33 tff(11167,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(z))))) | (~b(z, s(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(X0, 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(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11168,plain,
% 2.13/2.33 (((~b(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(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11169,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[11168])).
% 2.13/2.33 tff(11170,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[11169, 11167])).
% 2.13/2.33 tff(11171,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(11172,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11171, 11170])).
% 2.13/2.33 tff(11173,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11172, 245, 11166, 11164, 11156, 11141])).
% 2.13/2.33 tff(11174,plain,((~b(s(z), s(elem!1))) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (s(s(s(z))) = elem!1) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(11175,plain,
% 2.13/2.33 ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11174, 10862, 11060])).
% 2.13/2.33 tff(11176,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11175, 11126, 11119, 11105, 10673, 4186, 11101, 10955])).
% 2.13/2.33 tff(11177,plain,((~r(z, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(11178,plain,
% 2.13/2.33 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11177, 106, 4186, 130, 1368])).
% 2.13/2.33 tff(11179,plain,
% 2.13/2.33 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1992, 11178])).
% 2.13/2.33 tff(11180,plain,
% 2.13/2.33 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(elem!1))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10765])).
% 2.13/2.33 tff(11181,plain,
% 2.13/2.33 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(symmetry,[status(thm)],[11180])).
% 2.13/2.33 tff(11182,plain,
% 2.13/2.33 ((~r(s(z), s(s(s(s(elem!1)))))) <=> (~r(s(z), s(elem!1)))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10918])).
% 2.13/2.33 tff(11183,plain,
% 2.13/2.33 (~r(z, elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[649, 10949, 572])).
% 2.13/2.33 tff(11184,plain,
% 2.13/2.33 (b(z, elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[175, 11183, 10857])).
% 2.13/2.33 tff(11185,plain,
% 2.13/2.33 (~(s(elem!1) = s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[347, 10858])).
% 2.13/2.33 tff(11186,plain,
% 2.13/2.33 (b(z, s(elem!1)) <=> b(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[3835])).
% 2.13/2.33 tff(11187,plain,
% 2.13/2.33 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(elem!1))),
% 2.13/2.33 inference(symmetry,[status(thm)],[11186])).
% 2.13/2.33 tff(11188,plain,
% 2.13/2.33 (b(z, s(elem!1))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[2197, 11187])).
% 2.13/2.33 tff(11189,plain,
% 2.13/2.33 (~b(s(z), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4216, 11188, 4186, 10789, 572, 11185, 11184, 4187])).
% 2.13/2.33 tff(11190,plain,
% 2.13/2.33 (r(s(z), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[232, 11189])).
% 2.13/2.33 tff(11191,plain,
% 2.13/2.33 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3376, 141, 11190, 106])).
% 2.13/2.33 tff(11192,plain,
% 2.13/2.33 (~r(s(z), s(elem!1))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11191, 11182])).
% 2.13/2.33 tff(11193,plain,
% 2.13/2.33 (b(s(z), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[440, 11192, 10858])).
% 2.13/2.33 tff(11194,plain,
% 2.13/2.33 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11193, 11181])).
% 2.13/2.33 tff(11195,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(elem!1), s(z))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10765])).
% 2.13/2.33 tff(11196,plain,
% 2.13/2.33 (b(s(elem!1), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(symmetry,[status(thm)],[11195])).
% 2.13/2.33 tff(11197,plain,
% 2.13/2.33 ((~r(s(s(s(s(elem!1)))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10990])).
% 2.13/2.33 tff(11198,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[223, 141, 11190, 106])).
% 2.13/2.33 tff(11199,plain,
% 2.13/2.33 (~r(s(elem!1), s(z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11198, 11197])).
% 2.13/2.33 tff(11200,plain,
% 2.13/2.33 (b(s(elem!1), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[369, 11199, 11185])).
% 2.13/2.33 tff(11201,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11200, 11196])).
% 2.13/2.33 tff(11202,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11203,plain,
% 2.13/2.33 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11204,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[11203])).
% 2.13/2.33 tff(11205,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[11204, 11202])).
% 2.13/2.33 tff(11206,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(11207,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11206, 11205])).
% 2.13/2.33 tff(11208,plain,
% 2.13/2.33 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11207, 245, 2197, 4187])).
% 2.13/2.33 tff(11209,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11208, 11201, 11194])).
% 2.13/2.33 tff(11210,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~(s(elem!1) = s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(11211,plain,
% 2.13/2.33 ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~r(s(elem!1), elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11210, 10651])).
% 2.13/2.33 tff(11212,plain,
% 2.13/2.33 (~b(z, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11211, 11179, 106, 10673, 4186])).
% 2.13/2.33 tff(11213,plain,
% 2.13/2.33 (r(z, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1421, 11212])).
% 2.13/2.33 tff(11214,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4226, 11213, 106])).
% 2.13/2.33 tff(11215,plain,
% 2.13/2.33 (~r(s(elem!1), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10995, 11214])).
% 2.13/2.33 tff(11216,plain,
% 2.13/2.33 (b(s(elem!1), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10725, 11215])).
% 2.13/2.33 tff(11217,plain,
% 2.13/2.33 (~b(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7284, 4878, 4186, 10955])).
% 2.13/2.33 tff(11218,plain,
% 2.13/2.33 (r(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10872, 11217])).
% 2.13/2.33 tff(11219,plain,
% 2.13/2.33 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11099, 11218, 106, 4186, 130, 1368])).
% 2.13/2.33 tff(11220,plain,
% 2.13/2.33 (((~![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(s(z))))), z)) | (~r(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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(11221,plain,
% 2.13/2.33 ((~![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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(11222,plain,
% 2.13/2.33 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11221, 11220])).
% 2.13/2.33 tff(11223,plain,
% 2.13/2.33 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11222, 141, 106, 722])).
% 2.13/2.33 tff(11224,plain,
% 2.13/2.33 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10791, 3835])).
% 2.13/2.33 tff(11225,plain,
% 2.13/2.33 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10766])).
% 2.13/2.33 tff(11226,plain,
% 2.13/2.33 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[11225])).
% 2.13/2.33 tff(11227,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.13/2.33 tff(11228,plain,
% 2.13/2.33 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11227, 11226])).
% 2.13/2.33 tff(11229,plain,
% 2.13/2.33 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[797, 11228, 11224])).
% 2.13/2.33 tff(11230,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10772, 11229, 11223, 3835])).
% 2.13/2.33 tff(11231,plain,((~r(s(s(s(s(s(z))))), z)) | (~(s(elem!1) = s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(11232,plain,
% 2.13/2.33 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11231, 10651])).
% 2.13/2.33 tff(11233,plain,
% 2.13/2.33 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11232, 11219, 106])).
% 2.13/2.33 tff(11234,plain,
% 2.13/2.33 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[738, 11233])).
% 2.13/2.33 tff(11235,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6914, 245, 10955, 4186, 4878, 11234])).
% 2.13/2.33 tff(11236,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(11237,plain,
% 2.13/2.33 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11236, 106, 4186, 130, 1368])).
% 2.13/2.33 tff(11238,plain,
% 2.13/2.33 (r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10820, 11237])).
% 2.13/2.33 tff(11239,plain,
% 2.13/2.33 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10794, 11104])).
% 2.13/2.33 tff(11240,plain,
% 2.13/2.33 (~r(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11002, 2628, 4188, 10673, 655])).
% 2.13/2.33 tff(11241,plain,
% 2.13/2.33 (b(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10872, 11240])).
% 2.13/2.33 tff(11242,plain,
% 2.13/2.33 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11175, 11241, 4188, 10673, 4186, 655, 4105])).
% 2.13/2.33 tff(11243,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11242, 11239])).
% 2.13/2.33 tff(11244,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(11245,plain,
% 2.13/2.33 (~b(s(z), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11244, 11238, 11216, 4186, 130, 10955])).
% 2.13/2.33 tff(11246,plain,
% 2.13/2.33 (r(s(z), s(elem!1))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10926, 11245])).
% 2.13/2.33 tff(11247,plain,
% 2.13/2.33 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[11246, 10946])).
% 2.13/2.33 tff(11248,plain,
% 2.13/2.33 (~r(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[624, 11246, 10673])).
% 2.13/2.33 tff(11249,plain,
% 2.13/2.33 (b(s(z), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10872, 11248])).
% 2.13/2.33 tff(11250,plain,
% 2.13/2.33 (~b(s(z), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4436, 11249, 4186, 10955])).
% 2.13/2.33 tff(11251,plain,
% 2.13/2.33 (r(s(z), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[232, 11250])).
% 2.13/2.33 tff(11252,plain,
% 2.13/2.33 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3376, 141, 11251, 106])).
% 2.13/2.33 tff(11253,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[11252, 11247])).
% 2.13/2.34 tff(11254,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(11255,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11254, 10944, 130, 10703])).
% 2.13/2.34 tff(11256,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2558, 11255])).
% 2.13/2.34 tff(11257,plain,
% 2.13/2.34 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[11010])).
% 2.13/2.34 tff(11258,plain,
% 2.13/2.34 (b(s(s(s(s(s(s(s(elem!1))))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10662])).
% 2.13/2.34 tff(11259,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.13/2.34 inference(symmetry,[status(thm)],[11258])).
% 2.13/2.34 tff(11260,plain,
% 2.13/2.34 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[1943, 11259])).
% 2.13/2.34 tff(11261,plain,
% 2.13/2.34 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9370, 6192, 1943, 11260, 1993])).
% 2.13/2.34 tff(11262,plain,
% 2.13/2.34 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11024, 11261])).
% 2.13/2.34 tff(11263,plain,
% 2.13/2.34 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11262, 11008])).
% 2.13/2.34 tff(11264,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11263, 11257])).
% 2.13/2.34 tff(11265,plain,
% 2.13/2.34 (((~![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(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11266,plain,
% 2.13/2.34 (((~r(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(z)))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11267,plain,
% 2.13/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(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(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[11266])).
% 2.13/2.34 tff(11268,plain,
% 2.13/2.34 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(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(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(transitivity,[status(thm)],[11267, 11265])).
% 2.13/2.34 tff(11269,plain,
% 2.13/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(z))))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(11270,plain,
% 2.13/2.34 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11269, 11268])).
% 2.13/2.34 tff(11271,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11270, 141, 130, 2628])).
% 2.13/2.34 tff(11272,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11271, 11264])).
% 2.13/2.34 tff(11273,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(11274,plain,
% 2.13/2.34 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11273, 289, 130, 1943])).
% 2.13/2.34 tff(11275,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10820, 11274])).
% 2.13/2.34 tff(11276,plain,
% 2.13/2.34 (~b(elem!1, s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10907, 11275, 289, 130, 1943])).
% 2.13/2.34 tff(11277,plain,
% 2.13/2.34 (r(elem!1, s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10716, 11276])).
% 2.13/2.34 tff(11278,plain,
% 2.13/2.34 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[486, 10946])).
% 2.13/2.34 tff(11279,plain,
% 2.13/2.34 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2481, 141, 1368, 268])).
% 2.13/2.34 tff(11280,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11279, 11278])).
% 2.13/2.34 tff(11281,plain,((~r(s(z), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(11282,plain,
% 2.13/2.34 (~r(s(z), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11281, 11277, 1368])).
% 2.13/2.34 tff(11283,plain,
% 2.13/2.34 (b(s(z), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10926, 11282])).
% 2.13/2.34 tff(11284,plain,
% 2.13/2.34 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11283, 10655])).
% 2.13/2.34 tff(11285,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11286,plain,
% 2.13/2.34 (((~b(z, s(s(s(s(elem!1)))))) | (~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(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11287,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[11286])).
% 2.13/2.34 tff(11288,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.34 inference(transitivity,[status(thm)],[11287, 11285])).
% 2.13/2.34 tff(11289,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(11290,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11289, 11288])).
% 2.13/2.34 tff(11291,plain,
% 2.13/2.34 (~b(z, s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11290, 245, 1993, 1943, 11284])).
% 2.13/2.34 tff(11292,plain,
% 2.13/2.34 (r(z, s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1421, 11291])).
% 2.13/2.34 tff(11293,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6542, 141, 289, 11277, 11292])).
% 2.13/2.34 tff(11294,plain,((~r(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(11295,plain,
% 2.13/2.34 (~r(z, elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11294, 11256, 10703, 130])).
% 2.13/2.34 tff(11296,plain,
% 2.13/2.34 (b(z, elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10913, 11295])).
% 2.13/2.34 tff(11297,plain,
% 2.13/2.34 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.34 tff(11298,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), z) <=> b(s(elem!1), z)),
% 2.13/2.34 inference(symmetry,[status(thm)],[11297])).
% 2.13/2.34 tff(11299,plain,
% 2.13/2.34 (b(s(elem!1), z)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11256, 11298])).
% 2.13/2.34 tff(11300,plain,
% 2.13/2.34 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10656])).
% 2.13/2.34 tff(11301,plain,
% 2.13/2.34 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[11300])).
% 2.13/2.34 tff(11302,plain,
% 2.13/2.34 (b(z, s(s(s(elem!1))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11296, 11301])).
% 2.13/2.34 tff(11303,plain,
% 2.13/2.34 ((~b(s(z), z)) | (~r(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))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[379, 10724])).
% 2.13/2.34 tff(11304,plain,
% 2.13/2.34 (~b(s(z), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11303, 11302, 10682, 10937, 11299])).
% 2.13/2.34 tff(11305,plain,
% 2.13/2.34 (r(s(z), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[232, 11304])).
% 2.13/2.34 tff(11306,plain,
% 2.13/2.34 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(elem!1))),
% 2.13/2.34 inference(symmetry,[status(thm)],[10655])).
% 2.13/2.34 tff(11307,plain,
% 2.13/2.34 ((~b(s(z), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(elem!1)))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[11306])).
% 2.13/2.34 tff(11308,plain,
% 2.13/2.34 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[11007, 10654])).
% 2.13/2.34 tff(11309,plain,
% 2.13/2.34 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11271, 11012])).
% 2.13/2.34 tff(11310,plain,
% 2.13/2.34 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11024, 11309])).
% 2.13/2.34 tff(11311,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11310, 11308])).
% 2.13/2.34 tff(11312,plain,
% 2.13/2.34 (b(z, s(s(s(elem!1))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[4105, 11301])).
% 2.13/2.34 tff(11313,plain,
% 2.13/2.34 (b(s(elem!1), z)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[1943, 11298])).
% 2.13/2.34 tff(11314,plain,
% 2.13/2.34 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11310, 11007])).
% 2.13/2.34 tff(11315,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), 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(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11316,plain,
% 2.13/2.34 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11317,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[11316])).
% 2.13/2.34 tff(11318,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.34 inference(transitivity,[status(thm)],[11317, 11315])).
% 2.13/2.34 tff(11319,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(11320,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11319, 11318])).
% 2.13/2.34 tff(11321,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11320, 245, 235, 234, 288, 919, 6122])).
% 2.13/2.34 tff(11322,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(11323,plain,
% 2.13/2.34 (~b(s(s(s(s(s(z))))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11322, 11314, 234, 11313, 11312])).
% 2.13/2.34 tff(11324,plain,
% 2.13/2.34 (r(s(s(s(s(s(z))))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[738, 11323])).
% 2.13/2.34 tff(11325,plain,
% 2.13/2.34 (~r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7135, 141, 220, 11324])).
% 2.13/2.34 tff(11326,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[809, 11325])).
% 2.13/2.34 tff(11327,plain,
% 2.13/2.34 (~r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[5856, 141, 220, 11324])).
% 2.13/2.34 tff(11328,plain,
% 2.13/2.34 (b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1698, 11327])).
% 2.13/2.34 tff(11329,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11330,plain,
% 2.13/2.34 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11331,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[11330])).
% 2.13/2.34 tff(11332,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[11331, 11329])).
% 2.13/2.34 tff(11333,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(11334,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11333, 11332])).
% 2.13/2.34 tff(11335,plain,
% 2.13/2.34 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11334, 245, 11328, 11326, 11311])).
% 2.13/2.34 tff(11336,plain,
% 2.13/2.34 (~b(s(z), s(elem!1))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11335, 11307])).
% 2.13/2.34 tff(11337,plain,
% 2.13/2.34 (r(s(z), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10926, 11336])).
% 2.13/2.34 tff(11338,plain,
% 2.13/2.34 (~r(s(z), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[624, 11337, 10673])).
% 2.13/2.34 tff(11339,plain,
% 2.13/2.34 (b(s(z), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10872, 11338])).
% 2.13/2.34 tff(11340,plain,
% 2.13/2.34 (~b(s(s(s(z))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7253, 11339, 4186, 4105])).
% 2.13/2.34 tff(11341,plain,
% 2.13/2.34 (r(s(s(s(z))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10863, 11340])).
% 2.13/2.34 tff(11342,plain,
% 2.13/2.34 (~r(s(elem!1), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7260, 11341, 10673])).
% 2.13/2.34 tff(11343,plain,
% 2.13/2.34 (b(s(elem!1), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11061, 11342])).
% 2.13/2.34 tff(11344,plain,
% 2.13/2.34 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11117, 11337, 220])).
% 2.13/2.34 tff(11345,plain,
% 2.13/2.34 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1992, 11344])).
% 2.13/2.34 tff(11346,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10794, 10663])).
% 2.13/2.34 tff(11347,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11348,plain,
% 2.13/2.34 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11349,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[11348])).
% 2.13/2.34 tff(11350,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[11349, 11347])).
% 2.13/2.34 tff(11351,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(11352,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11351, 11350])).
% 2.13/2.34 tff(11353,plain,
% 2.13/2.34 ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11352, 245, 4105, 1943, 11346])).
% 2.13/2.34 tff(11354,plain,
% 2.13/2.34 (~b(z, s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11353, 11345])).
% 2.13/2.34 tff(11355,plain,
% 2.13/2.34 (r(z, s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[758, 11354])).
% 2.13/2.34 tff(11356,plain,
% 2.13/2.34 (~r(s(s(s(z))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7209, 11355, 220, 11328, 11326])).
% 2.13/2.34 tff(11357,plain,
% 2.13/2.34 (b(s(s(s(z))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7060, 11356])).
% 2.13/2.34 tff(11358,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10839, 245, 2197, 1943, 11070, 911])).
% 2.13/2.34 tff(11359,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(11360,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11359, 11357, 1943, 11345])).
% 2.13/2.34 tff(11361,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11068, 11360, 11343])).
% 2.13/2.34 tff(11362,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(11363,plain,
% 2.13/2.34 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[11362, 11256, 11305, 10944, 11296, 10937, 130])).
% 2.13/2.34 tff(11364,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10820, 11363])).
% 2.13/2.34 tff(11365,plain,
% 2.13/2.34 (~b(s(s(s(s(s(z))))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6914, 245, 11296, 10944, 11364])).
% 2.13/2.34 tff(11366,plain,
% 2.13/2.34 (r(s(s(s(s(s(z))))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[738, 11365])).
% 2.13/2.34 tff(11367,plain,
% 2.13/2.34 (~r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7135, 141, 11305, 11366])).
% 2.13/2.34 tff(11368,plain,
% 2.13/2.34 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[809, 11367])).
% 2.13/2.34 tff(11369,plain,
% 2.13/2.34 (~b(z, s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6989, 245, 11296, 10944, 11364])).
% 2.13/2.34 tff(11370,plain,
% 2.13/2.34 (r(z, s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[758, 11369])).
% 2.13/2.34 tff(11371,plain,
% 2.13/2.34 (~r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[5856, 141, 11305, 11366])).
% 2.13/2.34 tff(11372,plain,
% 2.13/2.34 (b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1698, 11371])).
% 2.13/2.34 tff(11373,plain,
% 2.13/2.34 (~r(s(s(s(z))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7209, 11372, 11305, 11370, 11368])).
% 2.13/2.34 tff(11374,plain,
% 2.13/2.34 (b(s(s(s(z))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7060, 11373])).
% 2.13/2.34 tff(11375,plain,
% 2.13/2.34 (~b(s(z), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[7284, 11364, 10944, 11296])).
% 2.13/2.34 tff(11376,plain,
% 2.13/2.34 (r(s(z), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10872, 11375])).
% 2.13/2.34 tff(11377,plain,
% 2.13/2.34 (~r(s(z), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10924, 11376, 10703])).
% 2.13/2.34 tff(11378,plain,
% 2.13/2.34 (b(s(z), s(elem!1))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10926, 11377])).
% 2.13/2.34 tff(11379,plain,
% 2.13/2.34 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[11378, 10655])).
% 2.13/2.34 tff(11380,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11381,plain,
% 2.13/2.34 (((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(11382,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11381])).
% 2.13/2.35 tff(11383,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[11382, 11380])).
% 2.13/2.35 tff(11384,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(11385,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11384, 11383])).
% 2.13/2.35 tff(11386,plain,
% 2.13/2.35 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11385, 245, 11296, 11256, 11379, 11364])).
% 2.13/2.35 tff(11387,plain,
% 2.13/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11386, 11368])).
% 2.13/2.35 tff(11388,plain,
% 2.13/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11387, 10665])).
% 2.13/2.35 tff(11389,plain,
% 2.13/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10793, 11388])).
% 2.13/2.35 tff(11390,plain,
% 2.13/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10773, 11389])).
% 2.13/2.35 tff(11391,plain,
% 2.13/2.35 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10979, 11390, 10703, 10944, 11296])).
% 2.13/2.35 tff(11392,plain,
% 2.13/2.35 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1992, 11391])).
% 2.13/2.35 tff(11393,plain,
% 2.13/2.35 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11359, 11392, 11256, 11374])).
% 2.13/2.35 tff(11394,plain,
% 2.13/2.35 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11068, 11393])).
% 2.13/2.35 tff(11395,plain,
% 2.13/2.35 (r(s(elem!1), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11061, 11394])).
% 2.13/2.35 tff(11396,plain,
% 2.13/2.35 (~r(s(s(s(z))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[7260, 11395, 10673])).
% 2.13/2.35 tff(11397,plain,
% 2.13/2.35 (b(s(s(s(z))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10863, 11396])).
% 2.13/2.35 tff(11398,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[7251, 245, 11296, 10944, 11374, 11397])).
% 2.13/2.35 tff(11399,plain,(b(elem!1, s(elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(11400,plain,
% 2.13/2.35 (b(elem!1, s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11399, 8921, 2338])).
% 2.13/2.35 tff(11401,plain,
% 2.13/2.35 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11400, 10666])).
% 2.13/2.35 tff(11402,plain,
% 2.13/2.35 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10656])).
% 2.13/2.35 tff(11403,plain,
% 2.13/2.35 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(symmetry,[status(thm)],[11402])).
% 2.13/2.35 tff(11404,plain,
% 2.13/2.35 ((~b(elem!1, z)) <=> (~b(s(s(s(elem!1))), z))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11403])).
% 2.13/2.35 tff(11405,plain,
% 2.13/2.35 (~r(s(elem!1), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[649, 289, 10673])).
% 2.13/2.35 tff(11406,plain,
% 2.13/2.35 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10952, 11405])).
% 2.13/2.35 tff(11407,plain,
% 2.13/2.35 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2558, 11406])).
% 2.13/2.35 tff(11408,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11409,plain,
% 2.13/2.35 (((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11410,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11409])).
% 2.13/2.35 tff(11411,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[11410, 11408])).
% 2.13/2.35 tff(11412,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(11413,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11412, 11411])).
% 2.13/2.35 tff(11414,plain,
% 2.13/2.35 (~b(elem!1, z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11413, 245, 1390, 1993, 11407])).
% 2.13/2.35 tff(11415,plain,
% 2.13/2.35 (~b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11414, 11404])).
% 2.13/2.35 tff(11416,plain,
% 2.13/2.35 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11273, 11407, 130, 289])).
% 2.13/2.35 tff(11417,plain,
% 2.13/2.35 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10820, 11416])).
% 2.13/2.35 tff(11418,plain,
% 2.13/2.35 (~b(elem!1, s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10907, 11417, 289, 130, 11407])).
% 2.13/2.35 tff(11419,plain,
% 2.13/2.35 (~r(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10748, 11418, 1993, 10673])).
% 2.13/2.35 tff(11420,plain,
% 2.13/2.35 (b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[37, 11419])).
% 2.13/2.35 tff(11421,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11420, 11415])).
% 2.13/2.35 tff(11422,plain,((~r(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(11423,plain,
% 2.13/2.35 (~r(z, elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11422, 11401, 8921])).
% 2.13/2.35 tff(11424,plain,
% 2.13/2.35 (b(z, elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10913, 11423])).
% 2.13/2.35 tff(11425,plain,
% 2.13/2.35 (~r(z, elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11422, 1390, 130])).
% 2.13/2.35 tff(11426,plain,
% 2.13/2.35 (b(z, elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10913, 11425])).
% 2.13/2.35 tff(11427,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11428,plain,
% 2.13/2.35 (((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11429,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11428])).
% 2.13/2.35 tff(11430,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[11429, 11427])).
% 2.13/2.35 tff(11431,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(11432,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11431, 11430])).
% 2.13/2.35 tff(11433,plain,
% 2.13/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11432, 245, 4105, 1390, 1943, 4878])).
% 2.13/2.35 tff(11434,plain,
% 2.13/2.35 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11433, 10665])).
% 2.13/2.35 tff(11435,plain,
% 2.13/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10793, 11434])).
% 2.13/2.35 tff(11436,plain,
% 2.13/2.35 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10773, 11435])).
% 2.13/2.35 tff(11437,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11438,plain,
% 2.13/2.35 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11439,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11438])).
% 2.13/2.35 tff(11440,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[11439, 11437])).
% 2.13/2.35 tff(11441,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(11442,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11441, 11440])).
% 2.13/2.35 tff(11443,plain,
% 2.13/2.35 (~b(z, s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11442, 245, 4105, 1390, 1943])).
% 2.13/2.35 tff(11444,plain,
% 2.13/2.35 (r(z, s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1992, 11443])).
% 2.13/2.35 tff(11445,plain,
% 2.13/2.35 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10958, 141, 11444, 11436])).
% 2.13/2.35 tff(11446,plain,
% 2.13/2.35 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[738, 11445])).
% 2.13/2.35 tff(11447,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11448,plain,
% 2.13/2.35 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11449,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11448])).
% 2.13/2.35 tff(11450,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[11449, 11447])).
% 2.13/2.35 tff(11451,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(11452,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11451, 11450])).
% 2.13/2.35 tff(11453,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11452, 245, 4105, 1390, 1943, 4878, 11446])).
% 2.13/2.35 tff(11454,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(11455,plain,
% 2.13/2.35 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11454, 10751, 1390, 11426])).
% 2.13/2.35 tff(11456,plain,
% 2.13/2.35 (r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10820, 11455])).
% 2.13/2.35 tff(11457,plain,
% 2.13/2.35 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10756, 141, 130, 11456])).
% 2.13/2.35 tff(11458,plain,
% 2.13/2.35 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10773, 11457])).
% 2.13/2.35 tff(11459,plain,
% 2.13/2.35 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10793, 11458])).
% 2.13/2.35 tff(11460,plain,
% 2.13/2.35 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11459, 10663])).
% 2.13/2.35 tff(11461,plain,
% 2.13/2.35 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[6809, 11456, 131])).
% 2.13/2.35 tff(11462,plain,
% 2.13/2.35 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[738, 11461])).
% 2.13/2.35 tff(11463,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11464,plain,
% 2.13/2.35 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(11465,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11464])).
% 2.13/2.35 tff(11466,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[11465, 11463])).
% 2.13/2.35 tff(11467,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(11468,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11467, 11466])).
% 2.13/2.35 tff(11469,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11468, 245, 11426, 1390, 10751, 11462, 11460])).
% 2.13/2.35 tff(11470,plain,((~r(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(11471,plain,
% 2.13/2.35 (~r(elem!1, z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11470, 1390, 130])).
% 2.13/2.35 tff(11472,plain,
% 2.13/2.35 (b(elem!1, z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10943, 11471])).
% 2.13/2.35 tff(11473,plain,
% 2.13/2.35 (~r(s(z), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[624, 619, 10673])).
% 2.13/2.35 tff(11474,plain,
% 2.13/2.35 (b(s(z), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10926, 11473])).
% 2.13/2.35 tff(11475,plain,
% 2.13/2.35 (~b(s(elem!1), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11244, 11474, 2628, 4186, 130, 4105])).
% 2.13/2.35 tff(11476,plain,
% 2.13/2.35 (r(s(elem!1), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10725, 11475])).
% 2.13/2.35 tff(11477,plain,
% 2.13/2.35 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10995, 11476])).
% 2.13/2.35 tff(11478,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10988, 141, 619, 130, 11477])).
% 2.13/2.35 tff(11479,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(11480,plain,
% 2.13/2.35 (~r(s(z), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11479, 2628, 130, 11472, 11426])).
% 2.13/2.35 tff(11481,plain,
% 2.13/2.35 (b(s(z), elem!1)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10872, 11480])).
% 2.13/2.35 tff(11482,plain,
% 2.13/2.35 (~b(s(z), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[4436, 11481, 11472, 11426])).
% 2.13/2.35 tff(11483,plain,
% 2.13/2.35 (r(s(z), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[232, 11482])).
% 2.13/2.35 tff(11484,plain,
% 2.13/2.35 (b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[11472, 11403])).
% 2.13/2.35 tff(11485,plain,
% 2.13/2.35 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11362, 11483, 11472, 2628, 11426, 11484, 130])).
% 2.13/2.35 tff(11486,plain,
% 2.13/2.35 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2558, 11485])).
% 2.13/2.35 tff(11487,plain,
% 2.13/2.35 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[225, 11486, 11483])).
% 2.13/2.35 tff(11488,plain,
% 2.13/2.35 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[217, 11487])).
% 2.13/2.35 tff(11489,plain,
% 2.13/2.35 (~b(s(z), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[4436, 447, 4186, 4105])).
% 2.13/2.35 tff(11490,plain,
% 2.13/2.35 (r(s(z), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[232, 11489])).
% 2.13/2.35 tff(11491,plain,
% 2.13/2.35 (~r(s(z), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11117, 11490, 310])).
% 2.13/2.35 tff(11492,plain,
% 2.13/2.35 (b(s(z), s(elem!1))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10926, 11491])).
% 2.13/2.35 tff(11493,plain,
% 2.13/2.35 (~b(z, s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[4595, 447, 4186, 4105])).
% 2.13/2.35 tff(11494,plain,
% 2.13/2.35 (r(z, s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1421, 11493])).
% 2.13/2.35 tff(11495,plain,
% 2.13/2.35 (~r(s(elem!1), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[4743, 11494, 11122])).
% 2.13/2.35 tff(11496,plain,
% 2.13/2.35 (b(s(elem!1), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10725, 11495])).
% 2.13/2.35 tff(11497,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[11244, 11496, 11492, 2628, 4186, 130, 4105])).
% 2.13/2.35 tff(11498,plain,((~b(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11499,plain,
% 2.13/2.36 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11498, 11481, 11472, 130, 11426, 2628])).
% 2.13/2.36 tff(11500,plain,
% 2.13/2.36 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1992, 11499])).
% 2.13/2.36 tff(11501,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11502,plain,
% 2.13/2.36 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11503,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11502])).
% 2.13/2.36 tff(11504,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11503, 11501])).
% 2.13/2.36 tff(11505,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11506,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11505, 11504])).
% 2.13/2.36 tff(11507,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11506, 245, 11426, 1390, 11481, 11500, 11488])).
% 2.13/2.36 tff(11508,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11509,plain,
% 2.13/2.36 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11508, 11401, 8921])).
% 2.13/2.36 tff(11510,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10820, 11509])).
% 2.13/2.36 tff(11511,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11454, 11510, 11401, 11424])).
% 2.13/2.36 tff(11512,plain,
% 2.13/2.36 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2558, 11511])).
% 2.13/2.36 tff(11513,plain,
% 2.13/2.36 (~r(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11470, 11401, 8921])).
% 2.13/2.36 tff(11514,plain,
% 2.13/2.36 (b(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10943, 11513])).
% 2.13/2.36 tff(11515,plain,
% 2.13/2.36 (~b(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[6914, 245, 11424, 11514, 11510])).
% 2.13/2.36 tff(11516,plain,
% 2.13/2.36 (r(s(s(s(s(s(z))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[738, 11515])).
% 2.13/2.36 tff(11517,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11232, 11516, 11512])).
% 2.13/2.36 tff(11518,plain,
% 2.13/2.36 (r(s(elem!1), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10672, 8921])).
% 2.13/2.36 tff(11519,plain,
% 2.13/2.36 (~b(s(z), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[7284, 11510, 11424, 11514])).
% 2.13/2.36 tff(11520,plain,
% 2.13/2.36 (r(s(z), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10872, 11519])).
% 2.13/2.36 tff(11521,plain,
% 2.13/2.36 (~r(s(z), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[624, 11520, 11518])).
% 2.13/2.36 tff(11522,plain,
% 2.13/2.36 (b(s(z), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10926, 11521])).
% 2.13/2.36 tff(11523,plain,
% 2.13/2.36 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11522, 10655])).
% 2.13/2.36 tff(11524,plain,
% 2.13/2.36 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10988, 141, 11520, 8921])).
% 2.13/2.36 tff(11525,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[217, 11524])).
% 2.13/2.36 tff(11526,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11527,plain,
% 2.13/2.36 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11528,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11527])).
% 2.13/2.36 tff(11529,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11528, 11526])).
% 2.13/2.36 tff(11530,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11531,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11530, 11529])).
% 2.13/2.36 tff(11532,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11531, 245, 11401, 11525, 11523, 11510, 11517])).
% 2.13/2.36 tff(11533,plain,((elem!1 = s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11534,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11533, 399])).
% 2.13/2.36 tff(11535,plain,
% 2.13/2.36 (~r(s(z), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8611, 619, 289])).
% 2.13/2.36 tff(11536,plain,
% 2.13/2.36 (b(s(z), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[232, 11535])).
% 2.13/2.36 tff(11537,plain,
% 2.13/2.36 (((~![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)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11538,plain,
% 2.13/2.36 (((~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)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11539,plain,
% 2.13/2.36 (((~![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))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11538])).
% 2.13/2.36 tff(11540,plain,
% 2.13/2.36 (((~![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)))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11539, 11537])).
% 2.13/2.36 tff(11541,plain,
% 2.13/2.36 ((~![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))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11542,plain,
% 2.13/2.36 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11541, 11540])).
% 2.13/2.36 tff(11543,plain,
% 2.13/2.36 (~r(z, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11542, 141, 289, 619])).
% 2.13/2.36 tff(11544,plain,
% 2.13/2.36 (b(z, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1421, 11543])).
% 2.13/2.36 tff(11545,plain,
% 2.13/2.36 (~b(s(s(s(z))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8573, 10325, 11544, 355])).
% 2.13/2.36 tff(11546,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[895, 32, 8431, 892, 11545])).
% 2.13/2.36 tff(11547,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11548,plain,
% 2.13/2.36 (~r(s(s(s(z))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11547, 11536, 289, 619])).
% 2.13/2.36 tff(11549,plain,
% 2.13/2.36 (b(s(s(s(z))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10863, 11548])).
% 2.13/2.36 tff(11550,plain,
% 2.13/2.36 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(symmetry,[status(thm)],[11007])).
% 2.13/2.36 tff(11551,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[10653, 11550])).
% 2.13/2.36 tff(11552,plain,
% 2.13/2.36 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z)))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11551])).
% 2.13/2.36 tff(11553,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11554,plain,
% 2.13/2.36 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(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(z)))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11555,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11554])).
% 2.13/2.36 tff(11556,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11555, 11553])).
% 2.13/2.36 tff(11557,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(z))))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11558,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11557, 11556])).
% 2.13/2.36 tff(11559,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11558, 245, 7788, 11534, 4878])).
% 2.13/2.36 tff(11560,plain,
% 2.13/2.36 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11559, 11552])).
% 2.13/2.36 tff(11561,plain,
% 2.13/2.36 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11024, 11560])).
% 2.13/2.36 tff(11562,plain,
% 2.13/2.36 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11561, 11008])).
% 2.13/2.36 tff(11563,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11564,plain,
% 2.13/2.36 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11565,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11564])).
% 2.13/2.36 tff(11566,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11565, 11563])).
% 2.13/2.36 tff(11567,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11568,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11567, 11566])).
% 2.13/2.36 tff(11569,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11568, 245, 7788, 11534, 954])).
% 2.13/2.36 tff(11570,plain,
% 2.13/2.36 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11068, 11569])).
% 2.13/2.36 tff(11571,plain,
% 2.13/2.36 (r(s(elem!1), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11061, 11570])).
% 2.13/2.36 tff(11572,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~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(X0, 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(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11573,plain,
% 2.13/2.36 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(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(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11574,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11573])).
% 2.13/2.36 tff(11575,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11574, 11572])).
% 2.13/2.36 tff(11576,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11577,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11576, 11575])).
% 2.13/2.36 tff(11578,plain,
% 2.13/2.36 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11577, 245, 7788, 11534, 4878, 954])).
% 2.13/2.36 tff(11579,plain,
% 2.13/2.36 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1515, 11578])).
% 2.13/2.36 tff(11580,plain,
% 2.13/2.36 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8472, 11579, 11571])).
% 2.13/2.36 tff(11581,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11580, 11562])).
% 2.13/2.36 tff(11582,plain,((elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | r(elem!1, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11583,plain,
% 2.13/2.36 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11582, 11549, 399, 4878])).
% 2.13/2.36 tff(11584,plain,
% 2.13/2.36 (~r(s(z), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10924, 11583, 619])).
% 2.13/2.36 tff(11585,plain,
% 2.13/2.36 (b(s(z), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10926, 11584])).
% 2.13/2.36 tff(11586,plain,
% 2.13/2.36 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11585, 10655])).
% 2.13/2.36 tff(11587,plain,
% 2.13/2.36 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[3688, 11583, 289])).
% 2.13/2.36 tff(11588,plain,
% 2.13/2.36 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1992, 11587])).
% 2.13/2.36 tff(11589,plain,
% 2.13/2.36 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.36 tff(11590,plain,
% 2.13/2.36 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(elem!1))),
% 2.13/2.36 inference(symmetry,[status(thm)],[11589])).
% 2.13/2.36 tff(11591,plain,
% 2.13/2.36 (r(elem!1, s(elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[1368, 11590])).
% 2.13/2.36 tff(11592,plain,
% 2.13/2.36 (~r(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1082, 131, 11591])).
% 2.13/2.36 tff(11593,plain,
% 2.13/2.36 (b(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1039, 11592])).
% 2.13/2.36 tff(11594,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2291, 11593, 8943, 655, 355, 2197])).
% 2.13/2.36 tff(11595,plain,((~r(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11596,plain,
% 2.13/2.37 (~r(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11595, 11585, 11536, 11588, 11583])).
% 2.13/2.37 tff(11597,plain,
% 2.13/2.37 (b(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10943, 11596])).
% 2.13/2.37 tff(11598,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11599,plain,
% 2.13/2.37 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11600,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11599])).
% 2.13/2.37 tff(11601,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11600, 11598])).
% 2.13/2.37 tff(11602,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11603,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11602, 11601])).
% 2.13/2.37 tff(11604,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11603, 245, 11597, 11536, 11588, 11534, 11586])).
% 2.13/2.37 tff(11605,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11606,plain,
% 2.13/2.37 (~r(s(z), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11605, 4878, 399, 289])).
% 2.13/2.37 tff(11607,plain,
% 2.13/2.37 (b(s(z), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10872, 11606])).
% 2.13/2.37 tff(11608,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.37 tff(11609,plain,
% 2.13/2.37 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11608])).
% 2.13/2.37 tff(11610,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(elem!1), s(z))),
% 2.13/2.37 inference(symmetry,[status(thm)],[10710])).
% 2.13/2.37 tff(11611,plain,
% 2.13/2.37 ((~b(s(s(s(s(elem!1)))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11610])).
% 2.13/2.37 tff(11612,plain,
% 2.13/2.37 (~b(s(elem!1), s(z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[4684, 11611])).
% 2.13/2.37 tff(11613,plain,
% 2.13/2.37 (r(s(elem!1), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10725, 11612])).
% 2.13/2.37 tff(11614,plain,
% 2.13/2.37 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1003, 11613, 6521])).
% 2.13/2.37 tff(11615,plain,
% 2.13/2.37 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11614, 11609])).
% 2.13/2.37 tff(11616,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11617,plain,
% 2.13/2.37 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11618,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11617])).
% 2.13/2.37 tff(11619,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11618, 11616])).
% 2.13/2.37 tff(11620,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11621,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11620, 11619])).
% 2.13/2.37 tff(11622,plain,
% 2.13/2.37 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11621, 245, 301, 447, 2824, 4878])).
% 2.13/2.37 tff(11623,plain,
% 2.13/2.37 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11622, 10665])).
% 2.13/2.37 tff(11624,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10793, 11623])).
% 2.13/2.37 tff(11625,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10773, 11624])).
% 2.13/2.37 tff(11626,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11625, 11615])).
% 2.13/2.37 tff(11627,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11628,plain,
% 2.13/2.37 (~b(elem!1, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11627, 11607, 11534, 4878])).
% 2.13/2.37 tff(11629,plain,
% 2.13/2.37 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10734, 11628])).
% 2.13/2.37 tff(11630,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[265, 11629])).
% 2.13/2.37 tff(11631,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11632,plain,
% 2.13/2.37 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11633,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11632])).
% 2.13/2.37 tff(11634,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11633, 11631])).
% 2.13/2.37 tff(11635,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11636,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11635, 11634])).
% 2.13/2.37 tff(11637,plain,
% 2.13/2.37 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11636, 245, 7788, 447, 11534, 4878])).
% 2.13/2.37 tff(11638,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[809, 11637])).
% 2.13/2.37 tff(11639,plain,
% 2.13/2.37 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2975, 245, 7788, 447, 11534])).
% 2.13/2.37 tff(11640,plain,
% 2.13/2.37 (~b(s(elem!1), s(z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11639, 11611])).
% 2.13/2.37 tff(11641,plain,
% 2.13/2.37 (r(s(elem!1), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10725, 11640])).
% 2.13/2.37 tff(11642,plain,
% 2.13/2.37 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1003, 11641, 11638])).
% 2.13/2.37 tff(11643,plain,
% 2.13/2.37 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11642, 11609])).
% 2.13/2.37 tff(11644,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11645,plain,
% 2.13/2.37 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), 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(z))))), elem!1)) | (~b(s(s(s(s(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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11646,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), 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(z))))), elem!1)) | (~b(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(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11645])).
% 2.13/2.37 tff(11647,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), 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(z))))), elem!1)) | (~b(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(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11646, 11644])).
% 2.13/2.37 tff(11648,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), 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(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11649,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11648, 11647])).
% 2.13/2.37 tff(11650,plain,
% 2.13/2.37 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11649, 245, 7788, 11534, 4878])).
% 2.13/2.37 tff(11651,plain,
% 2.13/2.37 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11650, 10665])).
% 2.13/2.37 tff(11652,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10793, 11651])).
% 2.13/2.37 tff(11653,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10773, 11652])).
% 2.13/2.37 tff(11654,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11653, 11643])).
% 2.13/2.37 tff(11655,plain,((elem!1 = s(s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | r(elem!1, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11656,plain,
% 2.13/2.37 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11655, 11607, 399, 4878])).
% 2.13/2.37 tff(11657,plain,
% 2.13/2.37 (r(elem!1, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10716, 11628])).
% 2.13/2.37 tff(11658,plain,
% 2.13/2.37 (~r(s(z), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11281, 11657, 11656])).
% 2.13/2.37 tff(11659,plain,
% 2.13/2.37 (b(s(z), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10926, 11658])).
% 2.13/2.37 tff(11660,plain,
% 2.13/2.37 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11659, 10655])).
% 2.13/2.37 tff(11661,plain,
% 2.13/2.37 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[3688, 11656, 289])).
% 2.13/2.37 tff(11662,plain,
% 2.13/2.37 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1992, 11661])).
% 2.13/2.37 tff(11663,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11664,plain,
% 2.13/2.37 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11665,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11664])).
% 2.13/2.37 tff(11666,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11665, 11663])).
% 2.13/2.37 tff(11667,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11668,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11667, 11666])).
% 2.13/2.37 tff(11669,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11668, 245, 4186, 447, 2197, 2824, 3380])).
% 2.13/2.37 tff(11670,plain,((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11671,plain,
% 2.13/2.37 (~b(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11670, 11607, 11662, 11534, 11660])).
% 2.13/2.37 tff(11672,plain,
% 2.13/2.37 (r(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10943, 11671])).
% 2.13/2.37 tff(11673,plain,
% 2.13/2.37 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(symmetry,[status(thm)],[10704])).
% 2.13/2.37 tff(11674,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[131, 11673])).
% 2.13/2.37 tff(11675,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[13, 11674])).
% 2.13/2.37 tff(11676,plain,((~r(elem!1, z)) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11677,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11676, 11672])).
% 2.13/2.37 tff(11678,plain,
% 2.13/2.37 (~b(s(z), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11595, 11672, 11659, 11662, 11656])).
% 2.13/2.37 tff(11679,plain,
% 2.13/2.37 (r(s(z), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[232, 11678])).
% 2.13/2.37 tff(11680,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2177, 11679, 11677, 11630])).
% 2.13/2.37 tff(11681,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11682,plain,
% 2.13/2.37 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11681, 289, 399])).
% 2.13/2.37 tff(11683,plain,
% 2.13/2.37 (r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10820, 11682])).
% 2.13/2.37 tff(11684,plain,
% 2.13/2.37 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[6190, 141, 289, 11683])).
% 2.13/2.37 tff(11685,plain,
% 2.13/2.37 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[738, 11684])).
% 2.13/2.37 tff(11686,plain,
% 2.13/2.37 (~b(z, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[6424, 11536, 289, 2628, 619])).
% 2.13/2.37 tff(11687,plain,
% 2.13/2.37 (r(z, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1421, 11686])).
% 2.13/2.37 tff(11688,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11542, 141, 289, 619, 11687])).
% 2.13/2.37 tff(11689,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11690,plain,
% 2.13/2.37 (~r(s(z), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11689, 11683, 289])).
% 2.13/2.37 tff(11691,plain,
% 2.13/2.37 (b(s(z), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10872, 11690])).
% 2.13/2.37 tff(11692,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11676, 131])).
% 2.13/2.37 tff(11693,plain,
% 2.13/2.37 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1432, 7787, 399])).
% 2.13/2.37 tff(11694,plain,
% 2.13/2.37 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), 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(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)))))) | (~b(s(z), elem!1)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11695,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), 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(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11694])).
% 2.13/2.37 tff(11696,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), 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(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11695, 4617])).
% 2.13/2.37 tff(11697,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), 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)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11698,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11697, 11696])).
% 2.13/2.37 tff(11699,plain,
% 2.13/2.37 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11698, 245, 11693, 11691, 11534])).
% 2.13/2.37 tff(11700,plain,
% 2.13/2.37 (~b(s(z), s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11699, 11307])).
% 2.13/2.37 tff(11701,plain,
% 2.13/2.37 (r(s(z), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10926, 11700])).
% 2.13/2.37 tff(11702,plain,
% 2.13/2.37 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11701, 10946])).
% 2.13/2.37 tff(11703,plain,
% 2.13/2.37 (~r(z, s(s(s(s(s(z))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[6119, 141, 289, 11683])).
% 2.13/2.37 tff(11704,plain,
% 2.13/2.37 (b(z, s(s(s(s(s(z))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[758, 11703])).
% 2.13/2.37 tff(11705,plain,
% 2.13/2.37 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[217, 11639])).
% 2.13/2.37 tff(11706,plain,
% 2.13/2.37 (~r(z, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[4226, 11705, 106])).
% 2.13/2.37 tff(11707,plain,
% 2.13/2.37 (b(z, s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1421, 11706])).
% 2.13/2.37 tff(11708,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[10701])).
% 2.13/2.37 tff(11709,plain,
% 2.13/2.37 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[10700])).
% 2.13/2.37 tff(11710,plain,
% 2.13/2.37 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11709, 11708])).
% 2.13/2.37 tff(11711,plain,
% 2.13/2.37 ((~r(elem!1, s(s(s(s(elem!1)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11710])).
% 2.13/2.37 tff(11712,plain,
% 2.13/2.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[7787, 11711])).
% 2.13/2.37 tff(11713,plain,
% 2.13/2.37 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[353, 2338, 11712])).
% 2.13/2.37 tff(11714,plain,
% 2.13/2.37 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[10651])).
% 2.13/2.37 tff(11715,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11714])).
% 2.13/2.37 tff(11716,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[10656])).
% 2.13/2.38 tff(11717,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[11716])).
% 2.13/2.38 tff(11718,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11717, 11715])).
% 2.13/2.38 tff(11719,plain,
% 2.13/2.38 (b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11534, 11718])).
% 2.13/2.38 tff(11720,plain,
% 2.13/2.38 ((~r(s(z), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4426, 10866])).
% 2.13/2.38 tff(11721,plain,
% 2.13/2.38 (~r(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11720, 11719, 1355, 10953, 11713])).
% 2.13/2.38 tff(11722,plain,
% 2.13/2.38 (b(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[232, 11721])).
% 2.13/2.38 tff(11723,plain,
% 2.13/2.38 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5957, 245, 11722, 11707, 919])).
% 2.13/2.38 tff(11724,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[809, 11723])).
% 2.13/2.38 tff(11725,plain,
% 2.13/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11726,plain,
% 2.13/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11727,plain,
% 2.13/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11726, 11725])).
% 2.13/2.38 tff(11728,plain,
% 2.13/2.38 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11727, 141, 11705, 11724])).
% 2.13/2.38 tff(11729,plain,
% 2.13/2.38 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10773, 11728])).
% 2.13/2.38 tff(11730,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10793, 11729])).
% 2.13/2.38 tff(11731,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11730, 11104])).
% 2.13/2.38 tff(11732,plain,
% 2.13/2.38 (b(s(elem!1), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[3835])).
% 2.13/2.38 tff(11733,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.13/2.38 inference(symmetry,[status(thm)],[11732])).
% 2.13/2.38 tff(11734,plain,
% 2.13/2.38 (b(s(elem!1), elem!1)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[2824, 11733])).
% 2.13/2.38 tff(11735,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[564, 11734])).
% 2.13/2.38 tff(11736,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | b(s(elem!1), elem!1) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11737,plain,
% 2.13/2.38 (b(s(elem!1), elem!1) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11736, 10651])).
% 2.13/2.38 tff(11738,plain,
% 2.13/2.38 (b(s(elem!1), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11737, 11534])).
% 2.13/2.38 tff(11739,plain,
% 2.13/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11740,plain,
% 2.13/2.38 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11741,plain,
% 2.13/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11740])).
% 2.13/2.38 tff(11742,plain,
% 2.13/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11741, 11739])).
% 2.13/2.38 tff(11743,plain,
% 2.13/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11744,plain,
% 2.13/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11743, 11742])).
% 2.13/2.38 tff(11745,plain,
% 2.13/2.38 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11744, 141, 11705, 11724])).
% 2.13/2.38 tff(11746,plain,
% 2.13/2.38 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11745, 11012])).
% 2.13/2.38 tff(11747,plain,
% 2.13/2.38 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11024, 11746])).
% 2.13/2.38 tff(11748,plain,
% 2.13/2.38 (b(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11747, 11007])).
% 2.13/2.38 tff(11749,plain,
% 2.13/2.38 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6147, 11060])).
% 2.13/2.38 tff(11750,plain,
% 2.13/2.38 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11749, 11748, 2222, 11738, 11731, 10953])).
% 2.13/2.38 tff(11751,plain,
% 2.13/2.38 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1515, 11750])).
% 2.13/2.38 tff(11752,plain,
% 2.13/2.38 (~b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5992, 245, 11722, 11707, 919])).
% 2.13/2.38 tff(11753,plain,
% 2.13/2.38 (r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1698, 11752])).
% 2.13/2.38 tff(11754,plain,
% 2.13/2.38 (~r(s(s(s(z))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6027, 141, 11753, 11751])).
% 2.13/2.38 tff(11755,plain,
% 2.13/2.38 (b(s(s(s(z))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[895, 32, 11754, 892])).
% 2.13/2.38 tff(11756,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11730, 10663])).
% 2.13/2.38 tff(11757,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11758,plain,
% 2.13/2.38 (((~b(elem!1, s(s(s(s(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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11759,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11758])).
% 2.13/2.38 tff(11760,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11759, 11757])).
% 2.13/2.38 tff(11761,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11762,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11761, 11760])).
% 2.13/2.38 tff(11763,plain,
% 2.13/2.38 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11762, 245, 7788, 11534, 11756])).
% 2.13/2.38 tff(11764,plain,
% 2.13/2.38 (r(elem!1, s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11051, 11763])).
% 2.13/2.38 tff(11765,plain,
% 2.13/2.38 (~r(s(s(s(z))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6167, 141, 11764, 11751])).
% 2.13/2.38 tff(11766,plain,
% 2.13/2.38 (b(s(s(s(z))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10863, 11765])).
% 2.13/2.38 tff(11767,plain,
% 2.13/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11768,plain,
% 2.13/2.38 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11769,plain,
% 2.13/2.38 (((~![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(elem!1, s(s(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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11768])).
% 2.13/2.38 tff(11770,plain,
% 2.13/2.38 (((~![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(elem!1, s(s(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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11769, 11767])).
% 2.13/2.38 tff(11771,plain,
% 2.13/2.38 ((~![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(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11772,plain,
% 2.13/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11771, 11770])).
% 2.13/2.38 tff(11773,plain,
% 2.13/2.38 (~r(elem!1, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11772, 141, 11764, 11753])).
% 2.13/2.38 tff(11774,plain,
% 2.13/2.38 (b(elem!1, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10716, 11773])).
% 2.13/2.38 tff(11775,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[884, 245, 11774, 447, 11766, 11755])).
% 2.13/2.38 tff(11776,plain,((elem!1 = s(s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | r(elem!1, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11777,plain,
% 2.13/2.38 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11776, 7787, 399, 11685, 11691, 11704, 1355])).
% 2.13/2.38 tff(11778,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2558, 11777])).
% 2.13/2.38 tff(11779,plain,
% 2.13/2.38 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3688, 310, 289])).
% 2.13/2.38 tff(11780,plain,
% 2.13/2.38 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1432, 11779, 399])).
% 2.13/2.38 tff(11781,plain,
% 2.13/2.38 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11698, 245, 11780, 11691, 11534])).
% 2.13/2.38 tff(11782,plain,
% 2.13/2.38 (~b(s(z), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11781, 11307])).
% 2.13/2.38 tff(11783,plain,
% 2.13/2.38 (r(s(z), s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10926, 11782])).
% 2.13/2.38 tff(11784,plain,
% 2.13/2.38 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11783, 10946])).
% 2.13/2.38 tff(11785,plain,
% 2.13/2.38 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11776, 11779, 399, 11685, 11691, 11704, 1355])).
% 2.13/2.38 tff(11786,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2558, 11785])).
% 2.13/2.38 tff(11787,plain,
% 2.13/2.38 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9350, 245, 11786, 11704, 11685])).
% 2.13/2.38 tff(11788,plain,
% 2.13/2.38 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11787, 10665])).
% 2.13/2.38 tff(11789,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10793, 11788])).
% 2.13/2.38 tff(11790,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10773, 11789])).
% 2.13/2.38 tff(11791,plain,
% 2.13/2.38 (((~![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(z))))), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11792,plain,
% 2.13/2.38 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11793,plain,
% 2.13/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11792])).
% 2.13/2.38 tff(11794,plain,
% 2.13/2.38 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11793, 11791])).
% 2.13/2.38 tff(11795,plain,
% 2.13/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11796,plain,
% 2.13/2.38 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11795, 11794])).
% 2.13/2.38 tff(11797,plain,
% 2.13/2.38 (~r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11796, 141, 11790, 11784])).
% 2.13/2.38 tff(11798,plain,
% 2.13/2.38 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2975, 245, 11780, 11691, 11534])).
% 2.13/2.38 tff(11799,plain,
% 2.13/2.38 (~b(s(elem!1), s(z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11798, 11611])).
% 2.13/2.38 tff(11800,plain,
% 2.13/2.38 (r(s(elem!1), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10725, 11799])).
% 2.13/2.38 tff(11801,plain,
% 2.13/2.38 (~r(z, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4743, 11800, 11122])).
% 2.13/2.38 tff(11802,plain,
% 2.13/2.38 (b(z, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1421, 11801])).
% 2.13/2.38 tff(11803,plain,
% 2.13/2.38 (~r(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11117, 11783, 310])).
% 2.13/2.38 tff(11804,plain,
% 2.13/2.38 (b(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[232, 11803])).
% 2.13/2.38 tff(11805,plain,
% 2.13/2.38 (~b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5992, 245, 11804, 11802, 11685])).
% 2.13/2.38 tff(11806,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1698, 11805, 11797])).
% 2.13/2.38 tff(11807,plain,((~r(z, s(s(s(s(elem!1)))))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11808,plain,
% 2.13/2.38 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11807, 1355, 399, 289])).
% 2.13/2.38 tff(11809,plain,
% 2.13/2.38 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1992, 11808])).
% 2.13/2.38 tff(11810,plain,
% 2.13/2.38 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9644, 245, 11809, 11778, 11685])).
% 2.13/2.38 tff(11811,plain,
% 2.13/2.38 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11810, 10665])).
% 2.13/2.38 tff(11812,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10793, 11811])).
% 2.13/2.38 tff(11813,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10773, 11812])).
% 2.13/2.38 tff(11814,plain,
% 2.13/2.38 (~r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8375, 141, 11813, 11702])).
% 2.13/2.38 tff(11815,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[809, 11814])).
% 2.13/2.38 tff(11816,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11817,plain,
% 2.13/2.38 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11818,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11817])).
% 2.13/2.38 tff(11819,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11818, 11816])).
% 2.13/2.38 tff(11820,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11821,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11820, 11819])).
% 2.13/2.38 tff(11822,plain,
% 2.13/2.38 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11821, 245, 11809, 11534, 11685])).
% 2.13/2.38 tff(11823,plain,
% 2.13/2.38 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11822, 11778])).
% 2.13/2.38 tff(11824,plain,
% 2.13/2.38 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11823, 11552])).
% 2.13/2.38 tff(11825,plain,
% 2.13/2.38 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11024, 11824])).
% 2.13/2.38 tff(11826,plain,
% 2.13/2.38 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11825, 11008])).
% 2.13/2.38 tff(11827,plain,
% 2.13/2.38 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2975, 245, 11693, 11691, 11534])).
% 2.13/2.38 tff(11828,plain,
% 2.13/2.38 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[217, 11827])).
% 2.13/2.38 tff(11829,plain,
% 2.13/2.38 (~r(s(z), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11796, 141, 11813, 11702])).
% 2.13/2.38 tff(11830,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(s(z))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1698, 11829])).
% 2.13/2.38 tff(11831,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11832,plain,
% 2.13/2.38 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11833,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11832])).
% 2.13/2.38 tff(11834,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11833, 11831])).
% 2.13/2.38 tff(11835,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11836,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11835, 11834])).
% 2.13/2.38 tff(11837,plain,
% 2.13/2.38 ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11836, 245, 11691, 11809, 11534, 11685])).
% 2.13/2.38 tff(11838,plain,
% 2.13/2.38 (~b(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11837, 11830])).
% 2.13/2.38 tff(11839,plain,
% 2.13/2.38 (r(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[232, 11838])).
% 2.13/2.38 tff(11840,plain,
% 2.13/2.38 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[10761])).
% 2.13/2.38 tff(11841,plain,
% 2.13/2.38 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[10784, 11840])).
% 2.13/2.38 tff(11842,plain,
% 2.13/2.38 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11841])).
% 2.13/2.38 tff(11843,plain,
% 2.13/2.38 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.38 inference(symmetry,[status(thm)],[11842])).
% 2.13/2.38 tff(11844,assumption,(b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.13/2.38 tff(11845,plain,
% 2.13/2.38 (b(s(s(s(z))), elem!1)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11844, 11843])).
% 2.13/2.38 tff(11846,plain,
% 2.13/2.38 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[10758])).
% 2.13/2.39 tff(11847,plain,
% 2.13/2.39 (b(s(z), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[2111, 11846])).
% 2.13/2.39 tff(11848,plain,
% 2.13/2.39 (b(elem!1, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10733, 2179, 10758])).
% 2.13/2.39 tff(11849,plain,
% 2.13/2.39 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[884, 245, 11848, 11847])).
% 2.13/2.39 tff(11850,plain,
% 2.13/2.39 (~b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11849, 11845])).
% 2.13/2.39 tff(11851,plain,
% 2.13/2.39 (r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[895, 32, 892, 11850])).
% 2.13/2.39 tff(11852,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 2.13/2.39 tff(11853,plain,
% 2.13/2.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11854,plain,
% 2.13/2.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11855,plain,
% 2.13/2.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11854, 11853])).
% 2.13/2.39 tff(11856,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11855, 141, 980, 11852, 219])).
% 2.13/2.39 tff(11857,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11858,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11857, 11851, 219])).
% 2.13/2.39 tff(11859,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10263, 11858, 10815])).
% 2.13/2.39 tff(11860,plain,
% 2.13/2.39 (~b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11359, 11859, 1943, 2197])).
% 2.13/2.39 tff(11861,plain,
% 2.13/2.39 (r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[836, 32, 833, 11860])).
% 2.13/2.39 tff(11862,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[983, 141, 220, 11851, 11861])).
% 2.13/2.39 tff(11863,plain,((~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~(s(elem!1) = s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11864,plain,
% 2.13/2.39 ((~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11863, 10651])).
% 2.13/2.39 tff(11865,plain,
% 2.13/2.39 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11864, 11839, 11809, 11778, 1355, 11828])).
% 2.13/2.39 tff(11866,plain,
% 2.13/2.39 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[876, 10861])).
% 2.13/2.39 tff(11867,plain,
% 2.13/2.39 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11866, 11865])).
% 2.13/2.39 tff(11868,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11841])).
% 2.13/2.39 tff(11869,plain,
% 2.13/2.39 (r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[11868])).
% 2.13/2.39 tff(11870,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[851, 11869])).
% 2.13/2.39 tff(11871,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[853, 11870])).
% 2.13/2.39 tff(11872,plain,((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(z))), elem!1) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11873,plain,
% 2.13/2.39 ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11872, 10651])).
% 2.13/2.39 tff(11874,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11873, 11867])).
% 2.13/2.39 tff(11875,plain,
% 2.13/2.39 (~r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10163, 11874, 289])).
% 2.13/2.39 tff(11876,plain,
% 2.13/2.39 (b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7060, 11875])).
% 2.13/2.39 tff(11877,plain,
% 2.13/2.39 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11359, 11876, 11809, 11778])).
% 2.13/2.39 tff(11878,plain,
% 2.13/2.39 (~b(s(elem!1), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11068, 11877])).
% 2.13/2.39 tff(11879,plain,
% 2.13/2.39 (r(s(elem!1), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11061, 11878])).
% 2.13/2.39 tff(11880,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8472, 11879, 11826])).
% 2.13/2.39 tff(11881,plain,
% 2.13/2.39 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1515, 11880])).
% 2.13/2.39 tff(11882,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6247, 245, 11876, 11830, 11881, 11704, 11815])).
% 2.13/2.39 tff(11883,plain,(r(elem!1, s(s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11884,plain,
% 2.13/2.39 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11883, 11692, 289, 399])).
% 2.13/2.39 tff(11885,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5214, 11884, 131])).
% 2.13/2.39 tff(11886,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2558, 11885])).
% 2.13/2.39 tff(11887,plain,
% 2.13/2.39 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11807, 11692, 399, 289])).
% 2.13/2.39 tff(11888,plain,
% 2.13/2.39 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1992, 11887])).
% 2.13/2.39 tff(11889,plain,
% 2.13/2.39 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9644, 245, 11888, 11886, 11685])).
% 2.13/2.39 tff(11890,plain,
% 2.13/2.39 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11889, 10665])).
% 2.13/2.39 tff(11891,plain,
% 2.13/2.39 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10793, 11890])).
% 2.13/2.39 tff(11892,plain,
% 2.13/2.39 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10773, 11891])).
% 2.13/2.39 tff(11893,plain,
% 2.13/2.39 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11894,plain,
% 2.13/2.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11895,plain,
% 2.13/2.39 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11894, 11893])).
% 2.13/2.39 tff(11896,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11895, 141, 11884, 11683, 11892])).
% 2.13/2.39 tff(11897,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11898,plain,
% 2.13/2.39 (~r(elem!1, z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11897, 289, 399])).
% 2.13/2.39 tff(11899,plain,
% 2.13/2.39 (b(elem!1, z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10943, 11898])).
% 2.13/2.39 tff(11900,plain,
% 2.13/2.39 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2975, 245, 1390, 447, 2824])).
% 2.13/2.39 tff(11901,plain,
% 2.13/2.39 (~b(s(elem!1), s(z))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11900, 11611])).
% 2.13/2.39 tff(11902,plain,
% 2.13/2.39 (r(s(elem!1), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10725, 11901])).
% 2.13/2.39 tff(11903,plain,
% 2.13/2.39 (b(s(s(s(elem!1))), z)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[4186, 11403])).
% 2.13/2.39 tff(11904,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[2824, 11717])).
% 2.13/2.39 tff(11905,plain,
% 2.13/2.39 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[10675])).
% 2.13/2.39 tff(11906,plain,
% 2.13/2.39 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1390, 11905])).
% 2.13/2.39 tff(11907,plain,
% 2.13/2.39 (~b(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8982, 11906, 11904, 11903])).
% 2.13/2.39 tff(11908,plain,
% 2.13/2.39 (r(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1992, 11907])).
% 2.13/2.39 tff(11909,plain,
% 2.13/2.39 (r(z, s(elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11908, 11121])).
% 2.13/2.39 tff(11910,plain,
% 2.13/2.39 (~r(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[4743, 11909, 11902])).
% 2.13/2.39 tff(11911,plain,
% 2.13/2.39 (b(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1421, 11910])).
% 2.13/2.39 tff(11912,plain,
% 2.13/2.39 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11698, 245, 1390, 447, 2824])).
% 2.13/2.39 tff(11913,plain,
% 2.13/2.39 (~b(s(z), s(elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11912, 11307])).
% 2.13/2.39 tff(11914,plain,
% 2.13/2.39 (r(s(z), s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10926, 11913])).
% 2.13/2.39 tff(11915,plain,
% 2.13/2.39 (~r(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11117, 11914, 11908])).
% 2.13/2.39 tff(11916,plain,
% 2.13/2.39 (b(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[232, 11915])).
% 2.13/2.39 tff(11917,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6571, 245, 4186, 11916, 447, 11911])).
% 2.13/2.39 tff(11918,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11919,plain,
% 2.13/2.39 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11918, 11899, 11691, 11534])).
% 2.13/2.39 tff(11920,plain,
% 2.13/2.39 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1432, 11919, 399])).
% 2.13/2.39 tff(11921,plain,
% 2.13/2.39 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3688, 11920, 289])).
% 2.13/2.39 tff(11922,plain,
% 2.13/2.39 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1992, 11921])).
% 2.13/2.39 tff(11923,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11924,plain,
% 2.13/2.39 (((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11925,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11924])).
% 2.13/2.39 tff(11926,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11925, 11923])).
% 2.13/2.39 tff(11927,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11928,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11927, 11926])).
% 2.13/2.39 tff(11929,plain,
% 2.13/2.39 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11928, 245, 11899, 11922, 11534, 11685])).
% 2.13/2.39 tff(11930,plain,
% 2.13/2.39 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11929, 10665])).
% 2.13/2.39 tff(11931,plain,
% 2.13/2.39 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10793, 11930])).
% 2.13/2.39 tff(11932,plain,
% 2.13/2.39 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10773, 11931])).
% 2.13/2.39 tff(11933,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11895, 141, 11920, 11683, 11932])).
% 2.13/2.39 tff(11934,plain,((~r(z, elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11935,plain,
% 2.13/2.39 (~r(z, elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11934, 399])).
% 2.13/2.39 tff(11936,plain,
% 2.13/2.39 (b(z, elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10913, 11935])).
% 2.13/2.39 tff(11937,plain,
% 2.13/2.39 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.39 inference(symmetry,[status(thm)],[10676])).
% 2.13/2.39 tff(11938,plain,
% 2.13/2.39 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11905, 11937])).
% 2.13/2.39 tff(11939,plain,
% 2.13/2.39 (b(s(s(s(elem!1))), s(elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1390, 11938])).
% 2.13/2.39 tff(11940,plain,
% 2.13/2.39 (b(elem!1, s(elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1390, 10674])).
% 2.13/2.39 tff(11941,plain,
% 2.13/2.39 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5379, 245, 4105, 1390, 2824])).
% 2.13/2.39 tff(11942,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2558, 11941])).
% 2.13/2.39 tff(11943,plain,
% 2.13/2.39 (~r(s(z), s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11117, 220, 310])).
% 2.13/2.39 tff(11944,plain,
% 2.13/2.39 (b(s(z), s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10926, 11943])).
% 2.13/2.39 tff(11945,plain,
% 2.13/2.39 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11944, 10655])).
% 2.13/2.39 tff(11946,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[983, 141, 220, 979])).
% 2.13/2.39 tff(11947,plain,
% 2.13/2.39 (b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[895, 32, 11946, 892])).
% 2.13/2.39 tff(11948,plain,
% 2.13/2.39 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11949,plain,
% 2.13/2.39 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11950,plain,
% 2.13/2.39 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11949, 11948])).
% 2.13/2.39 tff(11951,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11950, 141, 106, 979])).
% 2.13/2.39 tff(11952,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10263, 11951, 10257])).
% 2.13/2.39 tff(11953,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11954,plain,
% 2.13/2.39 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11955,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11954])).
% 2.13/2.39 tff(11956,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11955, 11953])).
% 2.13/2.39 tff(11957,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11958,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11957, 11956])).
% 2.13/2.39 tff(11959,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11958, 245, 2824, 11952, 4181, 3380, 11947])).
% 2.13/2.39 tff(11960,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11961,plain,
% 2.13/2.39 ((~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11960, 10822])).
% 2.13/2.39 tff(11962,plain,
% 2.13/2.39 (~r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11961, 11945, 2824, 106, 220])).
% 2.13/2.39 tff(11963,plain,
% 2.13/2.39 (b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7060, 11962])).
% 2.13/2.39 tff(11964,plain,
% 2.13/2.39 (b(s(elem!1), s(s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[2824, 11718])).
% 2.13/2.39 tff(11965,plain,
% 2.13/2.39 (~r(s(s(s(elem!1))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11720, 220, 11964, 10953, 1287])).
% 2.13/2.39 tff(11966,plain,
% 2.13/2.39 (~r(elem!1, z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11676, 11965])).
% 2.13/2.39 tff(11967,plain,
% 2.13/2.39 (b(elem!1, z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10943, 11966])).
% 2.13/2.39 tff(11968,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7251, 245, 4105, 4186, 911, 954])).
% 2.13/2.39 tff(11969,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11970,plain,
% 2.13/2.39 (~b(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11969, 11967, 4105, 11963])).
% 2.13/2.39 tff(11971,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10863, 11970])).
% 2.13/2.39 tff(11972,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8430, 11971, 619])).
% 2.13/2.39 tff(11973,plain,
% 2.13/2.39 (b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[895, 32, 11972, 892])).
% 2.13/2.39 tff(11974,plain,
% 2.13/2.39 (b(s(elem!1), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11737, 2824])).
% 2.13/2.39 tff(11975,plain,
% 2.13/2.39 (~b(elem!1, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5756, 11944, 1103, 11974])).
% 2.13/2.39 tff(11976,plain,
% 2.13/2.39 (r(elem!1, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10716, 11975])).
% 2.13/2.39 tff(11977,plain,
% 2.13/2.39 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11035, 245, 2653, 3380])).
% 2.13/2.39 tff(11978,plain,
% 2.13/2.39 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11977, 8808])).
% 2.13/2.39 tff(11979,plain,
% 2.13/2.39 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[808, 11978, 804])).
% 2.13/2.39 tff(11980,plain,
% 2.13/2.39 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5962, 141, 268, 11979])).
% 2.13/2.39 tff(11981,plain,
% 2.13/2.39 (b(s(s(s(s(s(z))))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[787, 11980, 1158])).
% 2.13/2.39 tff(11982,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11983,plain,
% 2.13/2.39 (((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11984,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11983])).
% 2.13/2.39 tff(11985,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11984, 11982])).
% 2.13/2.39 tff(11986,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11987,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11986, 11985])).
% 2.13/2.39 tff(11988,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11987, 245, 4105, 4186, 2824, 11981, 8808])).
% 2.13/2.39 tff(11989,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(s(z))))) = elem!1) | (~r(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11990,plain,
% 2.13/2.39 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11989, 10819])).
% 2.13/2.39 tff(11991,plain,
% 2.13/2.39 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11990, 11945, 2824, 4181, 11976, 11967, 4105])).
% 2.13/2.39 tff(11992,plain,
% 2.13/2.39 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11232, 11991, 106])).
% 2.13/2.39 tff(11993,plain,
% 2.13/2.39 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[738, 11992])).
% 2.13/2.39 tff(11994,plain,
% 2.13/2.39 (((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11995,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11994])).
% 2.23/2.40 tff(11996,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11995, 6909])).
% 2.23/2.40 tff(11997,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(11998,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11997, 11996])).
% 2.23/2.40 tff(11999,plain,
% 2.23/2.40 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11998, 245, 4105, 11967, 11993])).
% 2.23/2.40 tff(12000,plain,
% 2.23/2.40 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10820, 11999])).
% 2.23/2.40 tff(12001,plain,
% 2.23/2.40 (~r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6896, 141, 619, 12000])).
% 2.23/2.40 tff(12002,plain,
% 2.23/2.40 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[809, 12001])).
% 2.23/2.40 tff(12003,plain,
% 2.23/2.40 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7305, 141, 11971, 12000])).
% 2.23/2.40 tff(12004,plain,
% 2.23/2.40 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1515, 12003])).
% 2.23/2.40 tff(12005,plain,
% 2.23/2.40 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2649, 12000, 619])).
% 2.23/2.40 tff(12006,plain,
% 2.23/2.40 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1698, 12005])).
% 2.23/2.40 tff(12007,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6239, 245, 12006, 12004, 12002, 11973])).
% 2.23/2.40 tff(12008,plain,((~r(s(z), z)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12009,plain,
% 2.23/2.40 (~r(s(z), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12008, 11942, 4105, 619, 2824, 11940, 310, 11939])).
% 2.23/2.40 tff(12010,plain,
% 2.23/2.40 (b(s(z), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[232, 12009])).
% 2.23/2.40 tff(12011,plain,
% 2.23/2.40 (r(s(elem!1), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10952, 11942])).
% 2.23/2.40 tff(12012,plain,
% 2.23/2.40 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.23/2.40 inference(symmetry,[status(thm)],[9086])).
% 2.23/2.40 tff(12013,plain,
% 2.23/2.40 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.23/2.40 inference(transitivity,[status(thm)],[10999, 12012])).
% 2.23/2.40 tff(12014,plain,
% 2.23/2.40 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[12013])).
% 2.23/2.40 tff(12015,plain,
% 2.23/2.40 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[10792, 12014])).
% 2.23/2.40 tff(12016,plain,
% 2.23/2.40 ((~r(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5942, 12015, 10819])).
% 2.23/2.40 tff(12017,plain,
% 2.23/2.40 (~r(s(s(s(s(s(z))))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12016, 131, 11940, 12011, 11974])).
% 2.23/2.40 tff(12018,plain,
% 2.23/2.40 (b(s(s(s(s(s(z))))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[738, 12017])).
% 2.23/2.40 tff(12019,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12020,plain,
% 2.23/2.40 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12021,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[12020])).
% 2.23/2.40 tff(12022,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[12021, 12019])).
% 2.23/2.40 tff(12023,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(12024,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[12023, 12022])).
% 2.23/2.40 tff(12025,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12024, 245, 4105, 1390, 2824, 4878, 919])).
% 2.23/2.40 tff(12026,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, 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(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12027,plain,
% 2.23/2.40 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12026, 12018, 1390, 2824, 4105])).
% 2.23/2.40 tff(12028,plain,
% 2.23/2.40 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10820, 12027])).
% 2.23/2.40 tff(12029,plain,
% 2.23/2.40 (~r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6896, 141, 619, 12028])).
% 2.23/2.40 tff(12030,plain,
% 2.23/2.40 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[809, 12029])).
% 2.23/2.40 tff(12031,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8883, 245, 355, 4187, 709, 919])).
% 2.23/2.40 tff(12032,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12033,plain,
% 2.23/2.40 (~b(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12032, 12030, 355, 12018])).
% 2.23/2.40 tff(12034,plain,
% 2.23/2.40 (r(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1421, 12033])).
% 2.23/2.40 tff(12035,plain,
% 2.23/2.40 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[4226, 12034, 11942])).
% 2.23/2.40 tff(12036,plain,
% 2.23/2.40 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[217, 12035])).
% 2.23/2.40 tff(12037,plain,
% 2.23/2.40 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1457, 12034, 11692])).
% 2.23/2.40 tff(12038,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[265, 12037])).
% 2.23/2.40 tff(12039,plain,
% 2.23/2.40 (b(elem!1, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10734, 12038])).
% 2.23/2.40 tff(12040,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12041,plain,
% 2.23/2.40 (((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12042,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[12041])).
% 2.23/2.40 tff(12043,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[12042, 12040])).
% 2.23/2.40 tff(12044,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(12045,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[12044, 12043])).
% 2.23/2.40 tff(12046,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12045, 245, 4105, 12039, 355, 2824, 12036])).
% 2.23/2.40 tff(12047,plain,((~r(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12048,plain,
% 2.23/2.40 (~r(elem!1, z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12047, 12010, 4105, 2824, 619, 1390])).
% 2.23/2.40 tff(12049,plain,
% 2.23/2.40 (b(elem!1, z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10943, 12048])).
% 2.23/2.40 tff(12050,plain,
% 2.23/2.40 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11232, 722, 106])).
% 2.23/2.40 tff(12051,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11987, 245, 4105, 4186, 2824, 4878, 8808])).
% 2.23/2.40 tff(12052,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12053,plain,
% 2.23/2.40 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12052, 12050, 4105, 2824, 4186])).
% 2.23/2.40 tff(12054,plain,
% 2.23/2.40 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10820, 12053])).
% 2.23/2.40 tff(12055,plain,
% 2.23/2.40 (~r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6896, 141, 619, 12054])).
% 2.23/2.40 tff(12056,plain,
% 2.23/2.40 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[809, 12055])).
% 2.23/2.40 tff(12057,plain,
% 2.23/2.40 (r(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[836, 32, 833, 7058])).
% 2.23/2.40 tff(12058,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(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(X0, 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(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12059,plain,
% 2.23/2.40 (((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(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(z)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12060,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[12059])).
% 2.23/2.40 tff(12061,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[12060, 12058])).
% 2.23/2.40 tff(12062,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(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(z))))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(12063,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[12062, 12061])).
% 2.23/2.40 tff(12064,plain,
% 2.23/2.40 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12063, 245, 4105, 4186, 2824])).
% 2.23/2.40 tff(12065,plain,
% 2.23/2.40 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12064, 954])).
% 2.23/2.40 tff(12066,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10263, 12065, 10257])).
% 2.23/2.40 tff(12067,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11950, 141, 106, 12066, 12057])).
% 2.23/2.40 tff(12068,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12069,plain,
% 2.23/2.40 ((~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12068, 10822])).
% 2.23/2.40 tff(12070,plain,
% 2.23/2.40 (b(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12069, 954, 2824, 4105, 4186, 106])).
% 2.23/2.40 tff(12071,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11969, 12070, 954, 4105, 4186])).
% 2.23/2.40 tff(12072,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12073,plain,
% 2.23/2.40 (~b(s(s(s(z))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12072, 4186, 4105, 2824, 106])).
% 2.23/2.40 tff(12074,plain,
% 2.23/2.40 (r(s(s(s(z))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10863, 12073])).
% 2.23/2.40 tff(12075,plain,
% 2.23/2.40 (~r(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8430, 12074, 619])).
% 2.23/2.40 tff(12076,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 2.23/2.40 tff(12077,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[895, 32, 7233, 892, 12076])).
% 2.23/2.40 tff(12078,plain,(b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12079,plain,
% 2.23/2.40 (b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12078, 12075])).
% 2.23/2.40 tff(12080,plain,
% 2.23/2.40 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11020, 141, 106, 722])).
% 2.23/2.40 tff(12081,plain,
% 2.23/2.40 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[12080, 11012])).
% 2.23/2.40 tff(12082,plain,
% 2.23/2.40 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11024, 12081])).
% 2.23/2.40 tff(12083,plain,
% 2.23/2.40 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[12082, 11308])).
% 2.23/2.40 tff(12084,plain,
% 2.23/2.40 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2649, 12054, 619])).
% 2.23/2.40 tff(12085,plain,
% 2.23/2.40 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1698, 12084])).
% 2.23/2.40 tff(12086,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12087,plain,
% 2.23/2.40 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(12088,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[12087])).
% 2.23/2.40 tff(12089,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[12088, 12086])).
% 2.23/2.40 tff(12090,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(12091,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[12090, 12089])).
% 2.23/2.40 tff(12092,plain,
% 2.23/2.40 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12091, 245, 12085, 12056, 12083])).
% 2.23/2.40 tff(12093,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[217, 12092])).
% 2.23/2.40 tff(12094,plain,
% 2.23/2.40 (~r(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[4226, 12093, 106])).
% 2.23/2.40 tff(12095,plain,
% 2.23/2.40 (b(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1421, 12094])).
% 2.23/2.40 tff(12096,plain,
% 2.23/2.40 (~b(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8573, 8565, 4187, 355])).
% 2.23/2.40 tff(12097,plain,
% 2.23/2.40 (r(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7060, 12096])).
% 2.23/2.40 tff(12098,plain,
% 2.23/2.40 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7090, 12097, 740])).
% 2.23/2.40 tff(12099,plain,
% 2.23/2.40 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1515, 12098])).
% 2.23/2.40 tff(12100,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8583, 245, 355, 4187, 12099, 709, 8565])).
% 2.23/2.40 tff(12101,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(12102,plain,
% 2.23/2.40 (~r(z, s(s(s(s(s(z))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[12101, 12095, 355, 12079, 12056])).
% 2.23/2.40 tff(12103,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~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))))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12104,plain,
% 2.23/2.41 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~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, elem!1)) | (~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))))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12105,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12104])).
% 2.23/2.41 tff(12106,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~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))))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[12105, 12103])).
% 2.23/2.41 tff(12107,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(12108,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12107, 12106])).
% 2.23/2.41 tff(12109,plain,
% 2.23/2.41 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12108, 245, 4105, 355, 12056])).
% 2.23/2.41 tff(12110,plain,
% 2.23/2.41 (~b(z, s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12109, 12095])).
% 2.23/2.41 tff(12111,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[758, 12110, 12102])).
% 2.23/2.41 tff(12112,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12113,plain,
% 2.23/2.41 (~r(s(s(s(s(s(z))))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12112, 12010, 4105, 11942, 619, 2824, 12049])).
% 2.23/2.41 tff(12114,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[738, 12113])).
% 2.23/2.41 tff(12115,plain,
% 2.23/2.41 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12026, 12114, 1390, 2824, 4105])).
% 2.23/2.41 tff(12116,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10820, 12115])).
% 2.23/2.41 tff(12117,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2649, 12116, 619])).
% 2.23/2.41 tff(12118,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1698, 12117])).
% 2.23/2.41 tff(12119,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12120,plain,
% 2.23/2.41 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12121,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12120])).
% 2.23/2.41 tff(12122,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[12121, 12119])).
% 2.23/2.41 tff(12123,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(12124,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12123, 12122])).
% 2.23/2.41 tff(12125,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12124, 245, 4105, 12049, 12010, 12118, 12114])).
% 2.23/2.41 tff(12126,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12127,plain,
% 2.23/2.41 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12126, 3526, 619, 11534, 11936])).
% 2.23/2.41 tff(12128,plain,
% 2.23/2.41 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1432, 12127, 399])).
% 2.23/2.41 tff(12129,plain,
% 2.23/2.41 (~r(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4818, 12127, 11936, 3523])).
% 2.23/2.41 tff(12130,plain,
% 2.23/2.41 (b(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10943, 12129])).
% 2.23/2.41 tff(12131,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[11225])).
% 2.23/2.41 tff(12132,plain,
% 2.23/2.41 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10817, 3835])).
% 2.23/2.41 tff(12133,plain,
% 2.23/2.41 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10978, 1368, 4186, 12132, 4105, 310])).
% 2.23/2.41 tff(12134,plain,
% 2.23/2.41 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10772, 12133, 3835])).
% 2.23/2.41 tff(12135,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[797, 12134, 11224])).
% 2.23/2.41 tff(12136,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12135, 12131])).
% 2.23/2.41 tff(12137,plain,
% 2.23/2.41 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[3835])).
% 2.23/2.41 tff(12138,plain,
% 2.23/2.41 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.23/2.41 inference(transitivity,[status(thm)],[10787, 339])).
% 2.23/2.41 tff(12139,plain,
% 2.23/2.41 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12138])).
% 2.23/2.41 tff(12140,plain,
% 2.23/2.41 (~(s(z) = elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[1128, 12139])).
% 2.23/2.41 tff(12141,plain,
% 2.23/2.41 (~b(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4434, 245, 4105, 4186, 355])).
% 2.23/2.41 tff(12142,plain,
% 2.23/2.41 (r(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[389, 12141, 12140])).
% 2.23/2.41 tff(12143,plain,
% 2.23/2.41 (~r(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10923, 12142, 1368, 3835])).
% 2.23/2.41 tff(12144,plain,
% 2.23/2.41 (b(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[440, 12143, 9])).
% 2.23/2.41 tff(12145,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12144, 12137])).
% 2.23/2.41 tff(12146,plain,
% 2.23/2.41 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[775, 12132])).
% 2.23/2.41 tff(12147,plain,
% 2.23/2.41 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12052, 8808, 4186, 2824, 4105])).
% 2.23/2.41 tff(12148,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[787, 12147, 12146])).
% 2.23/2.41 tff(12149,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2649, 12142, 12148])).
% 2.23/2.41 tff(12150,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1697, 12149, 702])).
% 2.23/2.41 tff(12151,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12152,plain,
% 2.23/2.41 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12153,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12152])).
% 2.23/2.41 tff(12154,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[12153, 12151])).
% 2.23/2.41 tff(12155,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(12156,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12155, 12154])).
% 2.23/2.41 tff(12157,plain,
% 2.23/2.41 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12156, 245, 4186, 355, 2824, 8808])).
% 2.23/2.41 tff(12158,plain,
% 2.23/2.41 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12157, 12150])).
% 2.23/2.41 tff(12159,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12158, 12145])).
% 2.23/2.41 tff(12160,plain,((~b(s(z), z)) | (~(s(elem!1) = s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (s(z) = s(elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12161,plain,
% 2.23/2.41 (~b(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12160, 12136, 4186, 2824, 3835, 9, 1368, 4105])).
% 2.23/2.41 tff(12162,plain,
% 2.23/2.41 (r(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[232, 12161])).
% 2.23/2.41 tff(12163,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[225, 12162, 106])).
% 2.23/2.41 tff(12164,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[217, 12163])).
% 2.23/2.41 tff(12165,plain,
% 2.23/2.41 (~r(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11116, 12162, 310, 3835])).
% 2.23/2.41 tff(12166,plain,
% 2.23/2.41 (b(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[440, 12165, 9])).
% 2.23/2.41 tff(12167,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12166, 12137])).
% 2.23/2.41 tff(12168,plain,
% 2.23/2.41 (~r(elem!1, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11989, 12167, 4186, 2824, 12146, 12136, 12164, 4105])).
% 2.23/2.41 tff(12169,plain,
% 2.23/2.41 (~b(elem!1, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3388, 12167, 2824, 12164])).
% 2.23/2.41 tff(12170,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[281, 12169, 12168, 10789])).
% 2.23/2.41 tff(12171,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~(s(elem!1) = s(s(s(s(elem!1)))))) | (s(z) = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12172,plain,
% 2.23/2.41 ((~r(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12171, 10651, 10866])).
% 2.23/2.41 tff(12173,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12172, 12130, 11534, 11936, 12128, 3526])).
% 2.23/2.41 tff(12174,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2558, 12173])).
% 2.23/2.41 tff(12175,plain,
% 2.23/2.41 (b(s(elem!1), z)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12174, 11298])).
% 2.23/2.41 tff(12176,plain,
% 2.23/2.41 (~b(s(elem!1), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[7707, 12130, 11738, 11936])).
% 2.23/2.41 tff(12177,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12176, 12175])).
% 2.23/2.41 tff(12178,plain,(b(z, s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12179,plain,
% 2.23/2.41 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12178, 619, 399])).
% 2.23/2.41 tff(12180,plain,
% 2.23/2.41 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[619, 10707])).
% 2.23/2.41 tff(12181,plain,
% 2.23/2.41 (~r(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2109, 11692, 12180])).
% 2.23/2.41 tff(12182,plain,
% 2.23/2.41 (b(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[232, 12181])).
% 2.23/2.41 tff(12183,plain,
% 2.23/2.41 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12047, 12182, 11936, 11534, 619, 131])).
% 2.23/2.41 tff(12184,plain,
% 2.23/2.41 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1432, 12183, 399])).
% 2.23/2.41 tff(12185,plain,
% 2.23/2.41 (~r(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10924, 12184, 619])).
% 2.23/2.41 tff(12186,plain,
% 2.23/2.41 (~b(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11595, 12184, 12179, 131, 12182])).
% 2.23/2.41 tff(12187,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10926, 12186, 12185])).
% 2.23/2.41 tff(12188,plain,((~r(elem!1, z)) | (~r(s(z), elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12189,plain,
% 2.23/2.41 (~r(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12188, 619, 399])).
% 2.23/2.41 tff(12190,plain,
% 2.23/2.41 (b(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10943, 12189])).
% 2.23/2.41 tff(12191,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4903, 245, 11936, 12190, 12179, 11534])).
% 2.23/2.41 tff(12192,plain,((~r(s(z), elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12193,plain,
% 2.23/2.41 (~r(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12192, 399])).
% 2.23/2.41 tff(12194,plain,
% 2.23/2.41 (b(s(z), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10872, 12193])).
% 2.23/2.41 tff(12195,plain,
% 2.23/2.41 (~b(elem!1, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4687, 12194, 11534, 11936])).
% 2.23/2.41 tff(12196,plain,
% 2.23/2.41 (r(elem!1, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10716, 12195])).
% 2.23/2.41 tff(12197,plain,
% 2.23/2.41 (~b(s(s(s(elem!1))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10734, 12195])).
% 2.23/2.41 tff(12198,plain,
% 2.23/2.41 (r(s(s(s(elem!1))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[265, 12197])).
% 2.23/2.41 tff(12199,plain,
% 2.23/2.41 (~r(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1457, 11692, 12198])).
% 2.23/2.41 tff(12200,plain,
% 2.23/2.41 (b(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1421, 12199])).
% 2.23/2.41 tff(12201,plain,
% 2.23/2.41 (~r(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2177, 11692, 12198])).
% 2.23/2.41 tff(12202,plain,
% 2.23/2.41 (b(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[232, 12201])).
% 2.23/2.41 tff(12203,plain,
% 2.23/2.41 (~b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12032, 6811, 355, 4187])).
% 2.23/2.41 tff(12204,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[809, 12203])).
% 2.23/2.41 tff(12205,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5962, 141, 268, 2628, 12204])).
% 2.23/2.41 tff(12206,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12207,plain,
% 2.23/2.41 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12206, 12202, 12196, 12200, 131])).
% 2.23/2.41 tff(12208,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10820, 12207])).
% 2.23/2.41 tff(12209,plain,
% 2.23/2.41 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11655, 12208, 399, 12194])).
% 2.23/2.41 tff(12210,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5214, 12209, 131])).
% 2.23/2.41 tff(12211,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2558, 12210])).
% 2.23/2.41 tff(12212,plain,
% 2.23/2.41 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11454, 12211, 11936, 12208])).
% 2.23/2.41 tff(12213,plain,
% 2.23/2.41 (~r(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11281, 12209, 12196])).
% 2.23/2.41 tff(12214,plain,
% 2.23/2.41 (b(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10926, 12213])).
% 2.23/2.41 tff(12215,plain,
% 2.23/2.41 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11595, 12214, 12209, 131, 12202])).
% 2.23/2.41 tff(12216,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4818, 12215, 12212, 11936, 131])).
% 2.23/2.41 tff(12217,plain,((~r(elem!1, z)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12218,plain,
% 2.23/2.41 (~r(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12217, 399])).
% 2.23/2.41 tff(12219,plain,
% 2.23/2.41 (b(elem!1, z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10943, 12218])).
% 2.23/2.41 tff(12220,plain,
% 2.23/2.41 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11918, 12219, 12194, 11534])).
% 2.23/2.41 tff(12221,plain,
% 2.23/2.41 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1432, 12220, 399])).
% 2.23/2.41 tff(12222,plain,
% 2.23/2.41 (~r(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11281, 12221, 12196])).
% 2.23/2.41 tff(12223,plain,
% 2.23/2.41 (b(s(z), s(elem!1))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10926, 12222])).
% 2.23/2.41 tff(12224,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12223, 10655])).
% 2.23/2.41 tff(12225,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12226,plain,
% 2.23/2.41 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12227,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12226])).
% 2.23/2.41 tff(12228,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[12227, 12225])).
% 2.23/2.41 tff(12229,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(12230,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12229, 12228])).
% 2.23/2.41 tff(12231,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12230, 245, 11936, 12219, 12194, 11534, 12224])).
% 2.23/2.41 tff(12232,plain,(elem!1 = s(s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(12233,plain,
% 2.23/2.41 (elem!1 = s(elem!1)),
% 2.23/2.41 inference(transitivity,[status(thm)],[12232, 10652])).
% 2.23/2.41 tff(12234,plain,
% 2.23/2.41 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12233])).
% 2.23/2.41 tff(12235,plain,
% 2.23/2.41 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[12234, 10654])).
% 2.23/2.41 tff(12236,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12232])).
% 2.23/2.41 tff(12237,plain,
% 2.23/2.41 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(symmetry,[status(thm)],[12236])).
% 2.23/2.41 tff(12238,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.41 inference(symmetry,[status(thm)],[11608])).
% 2.23/2.41 tff(12239,plain,
% 2.23/2.41 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11227, 10665])).
% 2.23/2.41 tff(12240,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10793, 12239])).
% 2.23/2.41 tff(12241,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10773, 12240])).
% 2.23/2.41 tff(12242,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12241, 12238])).
% 2.23/2.41 tff(12243,plain,
% 2.23/2.41 (s(s(s(s(elem!1)))) = elem!1),
% 2.23/2.41 inference(symmetry,[status(thm)],[12232])).
% 2.23/2.41 tff(12244,plain,
% 2.23/2.41 (s(elem!1) = elem!1),
% 2.23/2.41 inference(transitivity,[status(thm)],[10651, 12243])).
% 2.23/2.41 tff(12245,plain,
% 2.23/2.41 (r(s(z), s(elem!1)) <=> r(s(z), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12244])).
% 2.23/2.41 tff(12246,plain,
% 2.23/2.41 (r(s(z), elem!1) <=> r(s(z), s(elem!1))),
% 2.23/2.41 inference(symmetry,[status(thm)],[12245])).
% 2.23/2.41 tff(12247,plain,
% 2.23/2.41 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[12246, 10946])).
% 2.23/2.41 tff(12248,plain,
% 2.23/2.41 (r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[619, 12247])).
% 2.23/2.41 tff(12249,plain,
% 2.23/2.41 ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[12237])).
% 2.23/2.41 tff(12250,plain,
% 2.23/2.41 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11227, 12249])).
% 2.23/2.41 tff(12251,plain,
% 2.23/2.41 (r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10820, 12250])).
% 2.23/2.41 tff(12252,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2649, 12251, 619])).
% 2.23/2.41 tff(12253,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1698, 12252])).
% 2.23/2.41 tff(12254,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.41 tff(12255,plain,
% 2.23/2.41 (((~![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(elem!1)))))) | (~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(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(z))))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(12256,plain,
% 2.23/2.41 ((~![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(elem!1)))))) | (~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(s(z))))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(12257,plain,
% 2.23/2.41 ((~![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(elem!1)))))) | (~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(s(z)))))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[12256, 12255])).
% 2.23/2.41 tff(12258,plain,
% 2.23/2.41 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[12257, 141, 8433, 12254])).
% 2.23/2.41 tff(12259,plain,
% 2.23/2.41 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 2.23/2.41 inference(commutativity,[status(thm)],[])).
% 2.23/2.41 tff(12260,plain,
% 2.23/2.41 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[12259])).
% 2.23/2.41 tff(12261,plain,
% 2.23/2.42 ((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12260])).
% 2.23/2.42 tff(12262,assumption,(s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 2.23/2.42 tff(12263,plain,
% 2.23/2.42 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12262])).
% 2.23/2.42 tff(12264,plain,
% 2.23/2.42 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[604, 12263, 2145, 12262])).
% 2.23/2.42 tff(12265,plain,
% 2.23/2.42 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12264])).
% 2.23/2.42 tff(12266,plain,
% 2.23/2.42 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[1043, 12265, 2145, 12262])).
% 2.23/2.42 tff(12267,assumption,(s(s(s(z))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 2.23/2.42 tff(12268,plain,
% 2.23/2.42 (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12267])).
% 2.23/2.42 tff(12269,plain,
% 2.23/2.42 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12267])).
% 2.23/2.42 tff(12270,plain,
% 2.23/2.42 (s(s(z)) = s(s(s(s(s(z)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[586, 12269, 2145])).
% 2.23/2.42 tff(12271,plain,
% 2.23/2.42 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12270])).
% 2.23/2.42 tff(12272,plain,
% 2.23/2.42 (s(z) = s(s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[591, 12271, 603, 12268])).
% 2.23/2.42 tff(12273,plain,
% 2.23/2.42 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12272])).
% 2.23/2.42 tff(12274,plain,
% 2.23/2.42 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 2.23/2.42 inference(symmetry,[status(thm)],[12273])).
% 2.23/2.42 tff(12275,plain,
% 2.23/2.42 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12276,plain,
% 2.23/2.42 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12275, 47])).
% 2.23/2.42 tff(12277,plain,
% 2.23/2.42 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.23/2.42 inference(symmetry,[status(thm)],[12276])).
% 2.23/2.42 tff(12278,plain,
% 2.23/2.42 (s(s(s(s(s(s(z)))))) = z),
% 2.23/2.42 inference(transitivity,[status(thm)],[12277, 12274, 52])).
% 2.23/2.42 tff(12279,plain,
% 2.23/2.42 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12280,plain,
% 2.23/2.42 (~(s(s(s(s(s(s(z)))))) = z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12279, 20])).
% 2.23/2.42 tff(12281,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12280, 12278])).
% 2.23/2.42 tff(12282,plain,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12283,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12282, 12266])).
% 2.23/2.42 tff(12284,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12285,plain,
% 2.23/2.42 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12284, 12261])).
% 2.23/2.42 tff(12286,plain,
% 2.23/2.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((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(s(z)))))) | r(s(s(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(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12287,plain,
% 2.23/2.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((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(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12288,plain,
% 2.23/2.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (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(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12287, 12286])).
% 2.23/2.42 tff(12289,plain,
% 2.23/2.42 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12288, 32, 12285, 12258])).
% 2.23/2.42 tff(12290,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.42 tff(12291,plain,
% 2.23/2.42 (((~![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(z), s(s(s(s(s(s(z)))))))) | (~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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12292,plain,
% 2.23/2.42 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12293,plain,
% 2.23/2.42 (((~![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(elem!1)))))) | (~r(s(z), s(s(s(s(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), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12292])).
% 2.23/2.42 tff(12294,plain,
% 2.23/2.42 (((~![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(elem!1)))))) | (~r(s(z), s(s(s(s(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), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[12293, 12291])).
% 2.23/2.42 tff(12295,plain,
% 2.23/2.42 ((~![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(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12296,plain,
% 2.23/2.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12295, 12294])).
% 2.23/2.42 tff(12297,plain,
% 2.23/2.42 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12296, 141, 12254, 12290])).
% 2.23/2.42 tff(12298,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 2.23/2.42 tff(12299,plain,
% 2.23/2.42 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12298])).
% 2.23/2.42 tff(12300,plain,
% 2.23/2.42 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 2.23/2.42 inference(symmetry,[status(thm)],[12299])).
% 2.23/2.42 tff(12301,plain,
% 2.23/2.42 (s(s(s(s(s(z))))) = z),
% 2.23/2.42 inference(transitivity,[status(thm)],[2278, 12300, 52])).
% 2.23/2.42 tff(12302,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[734, 12301])).
% 2.23/2.42 tff(12303,plain,(~(s(z) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12304,plain,
% 2.23/2.42 (((~![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))))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12305,plain,
% 2.23/2.42 ((~![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))))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12306,plain,
% 2.23/2.42 ((~![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)))))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12305, 12304])).
% 2.23/2.42 tff(12307,plain,
% 2.23/2.42 ((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)))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12306, 32])).
% 2.23/2.42 tff(12308,plain,
% 2.23/2.42 (b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12307, 12303])).
% 2.23/2.42 tff(12309,plain,
% 2.23/2.42 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12308, 12297])).
% 2.23/2.42 tff(12310,plain,
% 2.23/2.42 (~r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8375, 141, 8433, 12290])).
% 2.23/2.42 tff(12311,plain,
% 2.23/2.42 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[809, 12310])).
% 2.23/2.42 tff(12312,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12313,plain,
% 2.23/2.42 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12314,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12313])).
% 2.23/2.42 tff(12315,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[12314, 12312])).
% 2.23/2.42 tff(12316,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12317,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12316, 12315])).
% 2.23/2.42 tff(12318,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12317, 245, 6306, 12311, 12309, 12289])).
% 2.23/2.42 tff(12319,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12320,plain,
% 2.23/2.42 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12319, 12253, 12248, 12241])).
% 2.23/2.42 tff(12321,plain,
% 2.23/2.42 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12232])).
% 2.23/2.42 tff(12322,assumption,(r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 2.23/2.42 tff(12323,plain,
% 2.23/2.42 (r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12322, 12321])).
% 2.23/2.42 tff(12324,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.42 tff(12325,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12324, 12323])).
% 2.23/2.42 tff(12326,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12327,plain,
% 2.23/2.42 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12326, 12320])).
% 2.23/2.42 tff(12328,plain,
% 2.23/2.42 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(commutativity,[status(thm)],[])).
% 2.23/2.42 tff(12329,plain,
% 2.23/2.42 ((elem!1 = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.23/2.42 inference(symmetry,[status(thm)],[12328])).
% 2.23/2.42 tff(12330,plain,
% 2.23/2.42 ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12243])).
% 2.23/2.42 tff(12331,plain,
% 2.23/2.42 ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[12330, 12328])).
% 2.23/2.42 tff(12332,plain,
% 2.23/2.42 ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.23/2.42 inference(transitivity,[status(thm)],[12331, 12329])).
% 2.23/2.42 tff(12333,plain,
% 2.23/2.42 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12332])).
% 2.23/2.42 tff(12334,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.23/2.42 tff(12335,plain,
% 2.23/2.42 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12334])).
% 2.23/2.42 tff(12336,plain,
% 2.23/2.42 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(symmetry,[status(thm)],[12335])).
% 2.23/2.42 tff(12337,plain,
% 2.23/2.42 (elem!1 = s(s(s(elem!1)))),
% 2.23/2.42 inference(symmetry,[status(thm)],[10656])).
% 2.23/2.42 tff(12338,plain,
% 2.23/2.42 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[10651, 6408, 12337, 206, 12336, 2145])).
% 2.23/2.42 tff(12339,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11001, 12338])).
% 2.23/2.42 tff(12340,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12341,plain,
% 2.23/2.42 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12340, 12232])).
% 2.23/2.42 tff(12342,plain,
% 2.23/2.42 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12341, 12333])).
% 2.23/2.42 tff(12343,plain,
% 2.23/2.42 (((~![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))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12344,plain,
% 2.23/2.42 ((~![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))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12345,plain,
% 2.23/2.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12344, 12343])).
% 2.23/2.42 tff(12346,plain,
% 2.23/2.42 ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12345, 32])).
% 2.23/2.42 tff(12347,plain,
% 2.23/2.42 (b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12346, 12342])).
% 2.23/2.42 tff(12348,plain,
% 2.23/2.42 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12347, 12327])).
% 2.23/2.42 tff(12349,plain,
% 2.23/2.42 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12232])).
% 2.23/2.42 tff(12350,assumption,(b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 2.23/2.42 tff(12351,plain,
% 2.23/2.42 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12350, 12349])).
% 2.23/2.42 tff(12352,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.42 tff(12353,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12352, 12351])).
% 2.23/2.42 tff(12354,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12355,plain,
% 2.23/2.42 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12354, 12348])).
% 2.23/2.42 tff(12356,plain,
% 2.23/2.42 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12232])).
% 2.23/2.42 tff(12357,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(monotonicity,[status(thm)],[10660])).
% 2.23/2.42 tff(12358,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[12357, 12356])).
% 2.23/2.42 tff(12359,plain,
% 2.23/2.42 ((~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8453, 12232])).
% 2.23/2.42 tff(12360,plain,
% 2.23/2.42 (~r(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12359, 12253, 619, 12241])).
% 2.23/2.42 tff(12361,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11873, 12360])).
% 2.23/2.42 tff(12362,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11866, 12361])).
% 2.23/2.42 tff(12363,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12362, 12358])).
% 2.23/2.42 tff(12364,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 2.23/2.42 tff(12365,plain,
% 2.23/2.42 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[10651, 12364])).
% 2.23/2.42 tff(12366,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11001, 12365])).
% 2.23/2.42 tff(12367,plain,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12368,plain,
% 2.23/2.42 (b(z, elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[2197, 4804])).
% 2.23/2.42 tff(12369,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[90, 12368])).
% 2.23/2.42 tff(12370,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | b(z, elem!1) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12371,plain,
% 2.23/2.42 (b(z, elem!1) | (~b(z, s(s(s(s(elem!1))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12370, 12232])).
% 2.23/2.42 tff(12372,plain,
% 2.23/2.42 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12371, 90])).
% 2.23/2.42 tff(12373,plain,
% 2.23/2.42 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1992, 12372])).
% 2.23/2.42 tff(12374,plain,
% 2.23/2.42 (r(z, elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10913, 90])).
% 2.23/2.42 tff(12375,plain,
% 2.23/2.42 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 2.23/2.42 inference(monotonicity,[status(thm)],[10656])).
% 2.23/2.42 tff(12376,plain,
% 2.23/2.42 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 2.23/2.42 inference(symmetry,[status(thm)],[12375])).
% 2.23/2.42 tff(12377,plain,
% 2.23/2.42 (r(z, elem!1) <=> r(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12232])).
% 2.23/2.42 tff(12378,plain,
% 2.23/2.42 (r(z, s(s(s(s(elem!1))))) <=> r(z, elem!1)),
% 2.23/2.42 inference(symmetry,[status(thm)],[12377])).
% 2.23/2.42 tff(12379,plain,
% 2.23/2.42 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(elem!1))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[12378, 12376])).
% 2.23/2.42 tff(12380,plain,
% 2.23/2.42 (r(z, s(s(s(elem!1))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[310, 12379])).
% 2.23/2.42 tff(12381,plain,
% 2.23/2.42 (s(s(s(s(elem!1)))) = elem!1),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2567, 12232])).
% 2.23/2.42 tff(12382,plain,
% 2.23/2.42 ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6965, 12381])).
% 2.23/2.42 tff(12383,plain,
% 2.23/2.42 (~r(s(s(s(s(s(z))))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12382, 12240, 12380])).
% 2.23/2.42 tff(12384,plain,
% 2.23/2.42 (b(s(s(s(s(s(z))))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[738, 12383])).
% 2.23/2.42 tff(12385,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11162, 141, 980, 6013, 997])).
% 2.23/2.42 tff(12386,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12387,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12386, 6013, 997])).
% 2.23/2.42 tff(12388,plain,
% 2.23/2.42 (b(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12078, 12387])).
% 2.23/2.42 tff(12389,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12243])).
% 2.23/2.42 tff(12390,plain,
% 2.23/2.42 (b(elem!1, s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.42 inference(symmetry,[status(thm)],[12389])).
% 2.23/2.42 tff(12391,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12392,plain,
% 2.23/2.42 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12393,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(X0, 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(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12392])).
% 2.23/2.42 tff(12394,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(X0, 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(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[12393, 12391])).
% 2.23/2.42 tff(12395,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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))))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12396,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12395, 12394])).
% 2.23/2.42 tff(12397,plain,
% 2.23/2.42 ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12396, 245, 4187, 3380, 919])).
% 2.23/2.42 tff(12398,plain,
% 2.23/2.42 (~b(s(z), s(s(s(s(s(z))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12397, 355])).
% 2.23/2.42 tff(12399,plain,
% 2.23/2.42 (r(s(z), s(s(s(s(s(z))))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1698, 12398])).
% 2.23/2.42 tff(12400,plain,
% 2.23/2.42 (~r(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10903, 141, 12399, 6013])).
% 2.23/2.42 tff(12401,plain,
% 2.23/2.42 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10887, 32, 12400])).
% 2.23/2.42 tff(12402,plain,
% 2.23/2.42 (b(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12401, 10877])).
% 2.23/2.42 tff(12403,plain,
% 2.23/2.42 (~b(s(s(s(z))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8573, 355, 8565, 4187])).
% 2.23/2.42 tff(12404,plain,
% 2.23/2.42 (r(s(s(s(z))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[7060, 12403])).
% 2.23/2.42 tff(12405,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12406,plain,
% 2.23/2.42 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(12407,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(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(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[12406])).
% 2.23/2.42 tff(12408,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(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(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[12407, 12405])).
% 2.23/2.42 tff(12409,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(12410,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[12409, 12408])).
% 2.23/2.42 tff(12411,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12410, 245, 355, 1943, 4187, 3380])).
% 2.23/2.42 tff(12412,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(12413,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[12412, 355, 4187, 3380])).
% 2.23/2.42 tff(12414,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2558, 12413])).
% 2.23/2.42 tff(12415,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11950, 141, 12414, 12404])).
% 2.23/2.42 tff(12416,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10263, 10822])).
% 2.23/2.43 tff(12417,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12416, 12415])).
% 2.23/2.43 tff(12418,plain,
% 2.23/2.43 (~r(s(s(s(z))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10163, 12404, 289])).
% 2.23/2.43 tff(12419,plain,
% 2.23/2.43 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11873, 12418])).
% 2.23/2.43 tff(12420,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11866, 12419])).
% 2.23/2.43 tff(12421,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12420, 12358])).
% 2.23/2.43 tff(12422,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12423,plain,
% 2.23/2.43 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12424,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12423])).
% 2.23/2.43 tff(12425,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12424, 12422])).
% 2.23/2.43 tff(12426,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12427,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12426, 12425])).
% 2.23/2.43 tff(12428,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12427, 245, 12421, 12417, 3380, 12402])).
% 2.23/2.43 tff(12429,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12430,plain,
% 2.23/2.43 (~b(s(z), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12429, 4187, 3380, 6013, 289, 919, 12388])).
% 2.23/2.43 tff(12431,plain,
% 2.23/2.43 (r(s(z), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[232, 12430])).
% 2.23/2.43 tff(12432,plain,
% 2.23/2.43 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12433,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12432])).
% 2.23/2.43 tff(12434,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12433, 11030])).
% 2.23/2.43 tff(12435,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12436,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12435, 12434])).
% 2.23/2.43 tff(12437,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12436, 245, 2653, 3380, 709, 8808])).
% 2.23/2.43 tff(12438,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12439,plain,
% 2.23/2.43 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12438, 709, 3380, 8808])).
% 2.23/2.43 tff(12440,plain,
% 2.23/2.43 (~b(s(elem!1), s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12439, 11611])).
% 2.23/2.43 tff(12441,plain,
% 2.23/2.43 ((s(z) = s(elem!1)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[10651])).
% 2.23/2.43 tff(12442,plain,
% 2.23/2.43 ((s(z) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12441, 2435])).
% 2.23/2.43 tff(12443,plain,
% 2.23/2.43 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(elem!1))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12442])).
% 2.23/2.43 tff(12444,plain,
% 2.23/2.43 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(z))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12443, 10719])).
% 2.23/2.43 tff(12445,plain,
% 2.23/2.43 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12444])).
% 2.23/2.43 tff(12446,plain,
% 2.23/2.43 (~(s(elem!1) = s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[209, 12445])).
% 2.23/2.43 tff(12447,plain,
% 2.23/2.43 (b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[369, 12446])).
% 2.23/2.43 tff(12448,plain,
% 2.23/2.43 (r(s(elem!1), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12447, 12440])).
% 2.23/2.43 tff(12449,plain,
% 2.23/2.43 (~r(z, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[4743, 12448, 1342])).
% 2.23/2.43 tff(12450,plain,
% 2.23/2.43 (b(z, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1421, 12449])).
% 2.23/2.43 tff(12451,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12452,plain,
% 2.23/2.43 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12453,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12452])).
% 2.23/2.43 tff(12454,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12453, 12451])).
% 2.23/2.43 tff(12455,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12456,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12455, 12454])).
% 2.23/2.43 tff(12457,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12456, 245, 1943, 12450, 3380, 709, 8808])).
% 2.23/2.43 tff(12458,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12459,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12458, 8808, 3380, 1943, 1342])).
% 2.23/2.43 tff(12460,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[809, 12459])).
% 2.23/2.43 tff(12461,plain,
% 2.23/2.43 (~r(s(s(s(s(s(z))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6524, 141, 1449, 997])).
% 2.23/2.43 tff(12462,plain,
% 2.23/2.43 (b(s(s(s(s(s(z))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[738, 12461])).
% 2.23/2.43 tff(12463,plain,
% 2.23/2.43 (~r(z, s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11139, 141, 1449, 997])).
% 2.23/2.43 tff(12464,plain,
% 2.23/2.43 (b(z, s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[758, 12463])).
% 2.23/2.43 tff(12465,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9350, 245, 1943, 12464, 12462, 8808])).
% 2.23/2.43 tff(12466,plain,((~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12467,plain,
% 2.23/2.43 (~r(z, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12466, 8808, 1943, 12460])).
% 2.23/2.43 tff(12468,plain,
% 2.23/2.43 (b(z, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1421, 12467])).
% 2.23/2.43 tff(12469,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12470,plain,
% 2.23/2.43 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12471,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12470])).
% 2.23/2.43 tff(12472,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12471, 12469])).
% 2.23/2.43 tff(12473,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12474,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12473, 12472])).
% 2.23/2.43 tff(12475,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12474, 245, 1943, 12468, 3380, 8808])).
% 2.23/2.43 tff(12476,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[738, 12475])).
% 2.23/2.43 tff(12477,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7135, 141, 220, 12460, 12476])).
% 2.23/2.43 tff(12478,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12479,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12478, 220, 1943, 3380, 11122])).
% 2.23/2.43 tff(12480,plain,
% 2.23/2.43 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12479, 10665])).
% 2.23/2.43 tff(12481,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10793, 12480])).
% 2.23/2.43 tff(12482,plain,
% 2.23/2.43 (~r(s(s(s(s(s(z))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12382, 12481, 12380])).
% 2.23/2.43 tff(12483,plain,
% 2.23/2.43 (b(s(s(s(s(s(z))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[738, 12482])).
% 2.23/2.43 tff(12484,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10773, 12481])).
% 2.23/2.43 tff(12485,plain,
% 2.23/2.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12486,plain,
% 2.23/2.43 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12487,plain,
% 2.23/2.43 (((~![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(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12486])).
% 2.23/2.43 tff(12488,plain,
% 2.23/2.43 (((~![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(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12487, 12485])).
% 2.23/2.43 tff(12489,plain,
% 2.23/2.43 ((~![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(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12490,plain,
% 2.23/2.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12489, 12488])).
% 2.23/2.43 tff(12491,plain,
% 2.23/2.43 (~r(z, s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12490, 141, 310, 12484])).
% 2.23/2.43 tff(12492,plain,
% 2.23/2.43 (b(z, s(s(s(s(s(z))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[758, 12491])).
% 2.23/2.43 tff(12493,plain,
% 2.23/2.43 (r(s(s(s(s(s(z))))), s(elem!1))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12484, 12238])).
% 2.23/2.43 tff(12494,plain,
% 2.23/2.43 (~r(s(elem!1), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1003, 997, 12493])).
% 2.23/2.43 tff(12495,plain,
% 2.23/2.43 ((s(elem!1) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.23/2.43 inference(monotonicity,[status(thm)],[10651])).
% 2.23/2.43 tff(12496,plain,
% 2.23/2.43 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12495, 61])).
% 2.23/2.43 tff(12497,plain,
% 2.23/2.43 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(elem!1) = elem!1)),
% 2.23/2.43 inference(symmetry,[status(thm)],[12496])).
% 2.23/2.43 tff(12498,plain,
% 2.23/2.43 (s(elem!1) = elem!1),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12232, 12497])).
% 2.23/2.43 tff(12499,plain,
% 2.23/2.43 (r(s(elem!1), s(z)) <=> r(elem!1, s(z))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[97])).
% 2.23/2.43 tff(12500,plain,
% 2.23/2.43 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12499])).
% 2.23/2.43 tff(12501,plain,
% 2.23/2.43 (r(s(elem!1), s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[268, 12500])).
% 2.23/2.43 tff(12502,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 2.23/2.43 tff(12503,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12502, 12501])).
% 2.23/2.43 tff(12504,plain,((~(s(elem!1) = elem!1)) | r(s(elem!1), s(z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12505,plain,
% 2.23/2.43 (r(s(elem!1), s(z)) | (~r(elem!1, s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12504, 12498])).
% 2.23/2.43 tff(12506,plain,
% 2.23/2.43 (~r(elem!1, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12505, 12494])).
% 2.23/2.43 tff(12507,plain,
% 2.23/2.43 (b(elem!1, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10716, 12506])).
% 2.23/2.43 tff(12508,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12507, 12390])).
% 2.23/2.43 tff(12509,plain,
% 2.23/2.43 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[422])).
% 2.23/2.43 tff(12510,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12357, 12509])).
% 2.23/2.43 tff(12511,plain,
% 2.23/2.43 (~r(s(s(s(z))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10163, 979, 289])).
% 2.23/2.43 tff(12512,plain,
% 2.23/2.43 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11873, 12511])).
% 2.23/2.43 tff(12513,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11866, 12512])).
% 2.23/2.43 tff(12514,plain,
% 2.23/2.43 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12513, 12510])).
% 2.23/2.43 tff(12515,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12516,plain,
% 2.23/2.43 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12517,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12516])).
% 2.23/2.44 tff(12518,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12517, 12515])).
% 2.23/2.44 tff(12519,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12520,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12519, 12518])).
% 2.23/2.44 tff(12521,plain,
% 2.23/2.44 (~b(s(s(s(z))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12520, 245, 12514, 2653, 3380])).
% 2.23/2.44 tff(12522,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[895, 32, 7207, 892, 12521])).
% 2.23/2.44 tff(12523,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(12524,plain,
% 2.23/2.44 ((~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(z, elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12523, 12232])).
% 2.23/2.44 tff(12525,plain,
% 2.23/2.44 (~r(s(s(s(z))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12524, 12508, 220, 3380, 289])).
% 2.23/2.44 tff(12526,plain,
% 2.23/2.44 (b(s(s(s(z))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[7060, 12525])).
% 2.23/2.44 tff(12527,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(z, s(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(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12528,plain,
% 2.23/2.44 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12529,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12528])).
% 2.23/2.44 tff(12530,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12529, 12527])).
% 2.23/2.44 tff(12531,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12532,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12531, 12530])).
% 2.23/2.44 tff(12533,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12532, 245, 911, 6123, 2222, 919])).
% 2.23/2.44 tff(12534,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(12535,plain,
% 2.23/2.44 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12534, 12526, 12492, 12483])).
% 2.23/2.44 tff(12536,plain,
% 2.23/2.44 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1515, 12535])).
% 2.23/2.44 tff(12537,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12538,plain,
% 2.23/2.44 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12539,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12538])).
% 2.23/2.44 tff(12540,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12539, 12537])).
% 2.23/2.44 tff(12541,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12542,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12541, 12540])).
% 2.23/2.44 tff(12543,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12542, 245, 1943, 12492, 12483])).
% 2.23/2.44 tff(12544,plain,
% 2.23/2.44 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12543, 11552])).
% 2.23/2.44 tff(12545,plain,
% 2.23/2.44 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[11024, 12544])).
% 2.23/2.44 tff(12546,plain,
% 2.23/2.44 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12545, 11008])).
% 2.23/2.44 tff(12547,plain,
% 2.23/2.44 (~r(s(elem!1), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8472, 12536, 12546])).
% 2.23/2.44 tff(12548,plain,
% 2.23/2.44 (b(s(elem!1), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[11061, 12547])).
% 2.23/2.44 tff(12549,plain,
% 2.23/2.44 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[11068, 12548])).
% 2.23/2.44 tff(12550,plain,
% 2.23/2.44 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.44 inference(symmetry,[status(thm)],[12234])).
% 2.23/2.44 tff(12551,plain,
% 2.23/2.44 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[10653, 12550])).
% 2.23/2.44 tff(12552,plain,
% 2.23/2.44 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12551])).
% 2.23/2.44 tff(12553,plain,
% 2.23/2.44 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12543, 12552])).
% 2.23/2.44 tff(12554,plain,
% 2.23/2.44 (r(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[11051, 12553])).
% 2.23/2.44 tff(12555,plain,
% 2.23/2.44 (~r(elem!1, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[7550, 12536, 12554])).
% 2.23/2.44 tff(12556,plain,
% 2.23/2.44 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10845])).
% 2.23/2.44 tff(12557,plain,
% 2.23/2.44 (~(elem!1 = s(s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[10861, 12556])).
% 2.23/2.44 tff(12558,plain,
% 2.23/2.44 (b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[967, 12557])).
% 2.23/2.44 tff(12559,plain,
% 2.23/2.44 (b(elem!1, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12558, 12555])).
% 2.23/2.44 tff(12560,plain,
% 2.23/2.44 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[6408])).
% 2.23/2.44 tff(12561,plain,
% 2.23/2.44 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(symmetry,[status(thm)],[12560])).
% 2.23/2.44 tff(12562,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.23/2.44 tff(12563,plain,
% 2.23/2.44 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12562, 12561])).
% 2.23/2.44 tff(12564,plain,
% 2.23/2.44 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 2.23/2.44 inference(commutativity,[status(thm)],[])).
% 2.23/2.44 tff(12565,plain,
% 2.23/2.44 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 2.23/2.44 inference(symmetry,[status(thm)],[12564])).
% 2.23/2.44 tff(12566,plain,
% 2.23/2.44 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12565])).
% 2.23/2.44 tff(12567,plain,
% 2.23/2.44 (~(z = s(s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[833, 12566])).
% 2.23/2.44 tff(12568,assumption,(r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.44 tff(12569,plain,
% 2.23/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12570,plain,
% 2.23/2.44 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12571,plain,
% 2.23/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(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, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12570])).
% 2.23/2.44 tff(12572,plain,
% 2.23/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(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, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12571, 12569])).
% 2.23/2.44 tff(12573,plain,
% 2.23/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12574,plain,
% 2.23/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12573, 12572])).
% 2.23/2.44 tff(12575,plain,
% 2.23/2.44 ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12574, 141, 310])).
% 2.23/2.44 tff(12576,plain,
% 2.23/2.44 (~r(z, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12575, 12568])).
% 2.23/2.44 tff(12577,plain,
% 2.23/2.44 (((~![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)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12578,plain,
% 2.23/2.44 ((~![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)))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12579,plain,
% 2.23/2.44 ((~![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))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12578, 12577])).
% 2.23/2.44 tff(12580,plain,
% 2.23/2.44 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12579, 32, 12576])).
% 2.23/2.44 tff(12581,plain,
% 2.23/2.44 (b(z, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12580, 12567])).
% 2.23/2.44 tff(12582,plain,
% 2.23/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12583,plain,
% 2.23/2.44 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12584,plain,
% 2.23/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12583])).
% 2.23/2.44 tff(12585,plain,
% 2.23/2.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12584, 12582])).
% 2.23/2.44 tff(12586,plain,
% 2.23/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12587,plain,
% 2.23/2.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12586, 12585])).
% 2.23/2.44 tff(12588,plain,
% 2.23/2.44 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12587, 141, 310])).
% 2.23/2.44 tff(12589,plain,
% 2.23/2.44 (~r(s(s(s(z))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12588, 12568])).
% 2.23/2.44 tff(12590,plain,
% 2.23/2.44 (b(s(s(s(z))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[836, 32, 833, 12589])).
% 2.23/2.44 tff(12591,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12592,plain,
% 2.23/2.44 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12593,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12592])).
% 2.23/2.44 tff(12594,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12593, 12591])).
% 2.23/2.44 tff(12595,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12596,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12595, 12594])).
% 2.23/2.44 tff(12597,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12596, 245, 1943, 12590, 12581, 12563])).
% 2.23/2.44 tff(12598,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(z))))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(12599,plain,
% 2.23/2.44 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12598, 12232])).
% 2.23/2.44 tff(12600,plain,
% 2.23/2.44 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12599, 12559, 310, 1943])).
% 2.23/2.44 tff(12601,plain,
% 2.23/2.44 (r(s(s(s(z))), s(s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8442, 12232])).
% 2.23/2.44 tff(12602,plain,
% 2.23/2.44 (~r(s(s(s(z))), elem!1)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12601, 12600])).
% 2.23/2.44 tff(12603,plain,
% 2.23/2.44 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[11873, 12602])).
% 2.23/2.44 tff(12604,plain,
% 2.23/2.44 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[11866, 12603])).
% 2.23/2.44 tff(12605,plain,
% 2.23/2.44 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12604, 12358])).
% 2.23/2.44 tff(12606,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12607,plain,
% 2.23/2.44 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12608,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12607])).
% 2.23/2.44 tff(12609,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12608, 12606])).
% 2.23/2.44 tff(12610,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12611,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12610, 12609])).
% 2.23/2.45 tff(12612,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12611, 245, 12605, 12549, 3380])).
% 2.23/2.45 tff(12613,plain,
% 2.23/2.45 (r(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12078, 12612])).
% 2.23/2.45 tff(12614,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11162, 141, 12613, 12536, 997])).
% 2.23/2.45 tff(12615,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12616,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12615, 12431, 310, 3380, 997, 289])).
% 2.23/2.45 tff(12617,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2558, 12616])).
% 2.23/2.45 tff(12618,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[225, 12617, 12431])).
% 2.23/2.45 tff(12619,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[217, 12618])).
% 2.23/2.45 tff(12620,plain,
% 2.23/2.45 (~r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12524, 12619, 12431, 3380, 289])).
% 2.23/2.45 tff(12621,plain,
% 2.23/2.45 (b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[7060, 12620])).
% 2.23/2.45 tff(12622,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12623,plain,
% 2.23/2.45 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12624,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12623])).
% 2.23/2.45 tff(12625,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12624, 12622])).
% 2.23/2.45 tff(12626,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12627,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12626, 12625])).
% 2.23/2.45 tff(12628,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12627, 245, 4187, 12619, 3380, 12621, 12388])).
% 2.23/2.45 tff(12629,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12630,plain,
% 2.23/2.45 (~b(z, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12629, 12384, 289, 310, 997, 6013, 3380])).
% 2.23/2.45 tff(12631,plain,
% 2.23/2.45 (r(z, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1421, 12630])).
% 2.23/2.45 tff(12632,plain,
% 2.23/2.45 (~r(s(elem!1), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4743, 12631, 11122])).
% 2.23/2.45 tff(12633,plain,
% 2.23/2.45 (~r(elem!1, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12505, 12632])).
% 2.23/2.45 tff(12634,plain,
% 2.23/2.45 (b(elem!1, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10716, 12633])).
% 2.23/2.45 tff(12635,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12634, 12390])).
% 2.23/2.45 tff(12636,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8449, 141, 12568, 6013, 12241])).
% 2.23/2.45 tff(12637,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12638,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12637, 6013, 11227])).
% 2.23/2.45 tff(12639,plain,
% 2.23/2.45 (~r(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12601, 12638])).
% 2.23/2.45 tff(12640,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11873, 12639])).
% 2.23/2.45 tff(12641,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11866, 12640])).
% 2.23/2.45 tff(12642,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12641, 12358])).
% 2.23/2.45 tff(12643,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12520, 245, 12642, 12635, 3380, 12388])).
% 2.23/2.45 tff(12644,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12645,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12644, 997, 289, 310, 3380, 11227])).
% 2.23/2.45 tff(12646,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1515, 12645])).
% 2.23/2.45 tff(12647,plain,
% 2.23/2.45 (~r(z, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12490, 141, 310, 12241])).
% 2.23/2.45 tff(12648,plain,
% 2.23/2.45 (b(z, s(s(s(s(s(z))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[758, 12647])).
% 2.23/2.45 tff(12649,plain,
% 2.23/2.45 (~b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12534, 12648, 12646, 12384])).
% 2.23/2.45 tff(12650,plain,
% 2.23/2.45 (r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[7060, 12649])).
% 2.23/2.45 tff(12651,plain,
% 2.23/2.45 (~r(s(elem!1), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1003, 12242, 997])).
% 2.23/2.45 tff(12652,plain,
% 2.23/2.45 (~r(elem!1, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12505, 12651])).
% 2.23/2.45 tff(12653,plain,
% 2.23/2.45 (b(elem!1, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10716, 12652])).
% 2.23/2.45 tff(12654,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12653, 12390])).
% 2.23/2.45 tff(12655,plain,
% 2.23/2.45 (~r(s(s(s(z))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10163, 12650, 289])).
% 2.23/2.45 tff(12656,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11873, 12655])).
% 2.23/2.45 tff(12657,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11866, 12656])).
% 2.23/2.45 tff(12658,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12657, 12358])).
% 2.23/2.45 tff(12659,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12520, 245, 12658, 12654, 3380])).
% 2.23/2.45 tff(12660,plain,
% 2.23/2.45 (r(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12078, 12659])).
% 2.23/2.45 tff(12661,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 2.23/2.45 tff(12662,plain,
% 2.23/2.45 (s(s(s(z))) = z),
% 2.23/2.45 inference(symmetry,[status(thm)],[12661])).
% 2.23/2.45 tff(12663,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[833, 12662])).
% 2.23/2.45 tff(12664,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12665,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), z)) | (~b(z, s(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(X0, 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))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12666,plain,
% 2.23/2.45 (((~b(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(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12667,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12666])).
% 2.23/2.45 tff(12668,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12667, 12665])).
% 2.23/2.45 tff(12669,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12670,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12669, 12668])).
% 2.23/2.45 tff(12671,plain,
% 2.23/2.45 (~b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12670, 245, 12646, 12648, 12384])).
% 2.23/2.45 tff(12672,plain,
% 2.23/2.45 (r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12579, 32, 12671, 12664])).
% 2.23/2.45 tff(12673,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 2.23/2.45 tff(12674,plain,
% 2.23/2.45 (((~![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))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12675,plain,
% 2.23/2.45 (((~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))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12676,plain,
% 2.23/2.45 (((~![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)))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12675])).
% 2.23/2.45 tff(12677,plain,
% 2.23/2.45 (((~![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))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12676, 12674])).
% 2.23/2.45 tff(12678,plain,
% 2.23/2.45 ((~![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))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12679,plain,
% 2.23/2.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12678, 12677])).
% 2.23/2.45 tff(12680,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12679, 141, 1449, 980, 12673])).
% 2.23/2.45 tff(12681,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12682,plain,
% 2.23/2.45 (~r(z, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12681, 12672, 12660])).
% 2.23/2.45 tff(12683,plain,
% 2.23/2.45 (b(z, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1421, 12682])).
% 2.23/2.45 tff(12684,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5167, 12683, 3380, 12654])).
% 2.23/2.45 tff(12685,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2558, 12684])).
% 2.23/2.45 tff(12686,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11950, 141, 12685, 12650])).
% 2.23/2.45 tff(12687,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12416, 12686])).
% 2.23/2.45 tff(12688,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12689,plain,
% 2.23/2.45 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12690,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12689])).
% 2.23/2.45 tff(12691,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12690, 12688])).
% 2.23/2.45 tff(12692,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12693,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12692, 12691])).
% 2.23/2.45 tff(12694,plain,
% 2.23/2.45 (~b(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12693, 245, 12658, 12654, 3380])).
% 2.23/2.45 tff(12695,plain,
% 2.23/2.45 ((s(z) = s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10887, 32, 12694])).
% 2.23/2.45 tff(12696,plain,
% 2.23/2.45 (r(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12695, 10877])).
% 2.23/2.45 tff(12697,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 2.23/2.45 tff(12698,assumption,(b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.45 tff(12699,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.45 tff(12700,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.23/2.45 tff(12701,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12702,plain,
% 2.23/2.45 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12703,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12702])).
% 2.23/2.45 tff(12704,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12703, 12701])).
% 2.23/2.45 tff(12705,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12706,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12705, 12704])).
% 2.23/2.45 tff(12707,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12706, 245, 12698, 11070, 12700, 12699])).
% 2.23/2.45 tff(12708,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12709,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12708, 12699, 11070, 12698])).
% 2.23/2.45 tff(12710,plain,
% 2.23/2.45 (((~![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))))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12711,plain,
% 2.23/2.45 ((~![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))))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12712,plain,
% 2.23/2.45 ((~![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)))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12711, 12710])).
% 2.23/2.45 tff(12713,plain,
% 2.23/2.45 ((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)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12712, 32])).
% 2.23/2.45 tff(12714,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12713, 12282])).
% 2.23/2.45 tff(12715,plain,
% 2.23/2.45 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12714, 12709])).
% 2.23/2.45 tff(12716,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(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(X0, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12717,plain,
% 2.23/2.45 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12718,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(X0, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12717])).
% 2.23/2.45 tff(12719,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(X0, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12718, 12716])).
% 2.23/2.45 tff(12720,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12721,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12720, 12719])).
% 2.23/2.45 tff(12722,plain,
% 2.23/2.45 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12721, 245, 12698, 11070, 3380, 12699])).
% 2.23/2.45 tff(12723,plain,
% 2.23/2.45 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12308, 12722])).
% 2.23/2.45 tff(12724,plain,
% 2.23/2.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12725,plain,
% 2.23/2.46 (((~r(s(s(s(z))), s(s(s(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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12726,plain,
% 2.23/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12725])).
% 2.23/2.46 tff(12727,plain,
% 2.23/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12726, 12724])).
% 2.23/2.46 tff(12728,plain,
% 2.23/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12729,plain,
% 2.23/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12728, 12727])).
% 2.23/2.46 tff(12730,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12729, 141, 12723, 12715, 12697])).
% 2.23/2.46 tff(12731,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12732,plain,
% 2.23/2.46 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12731, 12696, 12658, 12687, 3380])).
% 2.23/2.46 tff(12733,plain,
% 2.23/2.46 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12354, 12732])).
% 2.23/2.46 tff(12734,plain,
% 2.23/2.46 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12347, 12733])).
% 2.23/2.46 tff(12735,plain,
% 2.23/2.46 (r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12326, 12734])).
% 2.23/2.46 tff(12736,plain,
% 2.23/2.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(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, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12737,plain,
% 2.23/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12738,plain,
% 2.23/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12737, 12736])).
% 2.23/2.46 tff(12739,plain,
% 2.23/2.46 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12738, 141, 310, 12735])).
% 2.23/2.46 tff(12740,plain,
% 2.23/2.46 (((~![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))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12741,plain,
% 2.23/2.46 ((~![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))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12742,plain,
% 2.23/2.46 ((~![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)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12741, 12740])).
% 2.23/2.46 tff(12743,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12742, 32, 12280, 12739])).
% 2.23/2.46 tff(12744,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.23/2.46 tff(12745,plain,
% 2.23/2.46 (((~![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(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(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(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12746,plain,
% 2.23/2.46 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12747,plain,
% 2.23/2.46 (((~![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(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(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(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12746])).
% 2.23/2.46 tff(12748,plain,
% 2.23/2.46 (((~![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(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(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(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12747, 12745])).
% 2.23/2.46 tff(12749,plain,
% 2.23/2.46 ((~![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(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12750,plain,
% 2.23/2.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12749, 12748])).
% 2.23/2.46 tff(12751,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12750, 141, 8433, 12744, 12254])).
% 2.23/2.46 tff(12752,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12753,plain,
% 2.23/2.46 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12752, 12735, 12241])).
% 2.23/2.46 tff(12754,plain,
% 2.23/2.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12755,plain,
% 2.23/2.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12756,plain,
% 2.23/2.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12755, 12754])).
% 2.23/2.46 tff(12757,plain,
% 2.23/2.46 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12756, 32])).
% 2.23/2.46 tff(12758,plain,
% 2.23/2.46 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12757, 12284])).
% 2.23/2.46 tff(12759,plain,
% 2.23/2.46 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12758, 12753])).
% 2.23/2.46 tff(12760,plain,
% 2.23/2.46 (~r(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12524, 12654, 12650, 3380, 289])).
% 2.23/2.46 tff(12761,plain,
% 2.23/2.46 (b(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[232, 12760])).
% 2.23/2.46 tff(12762,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(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(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12763,plain,
% 2.23/2.46 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12764,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(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(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12763])).
% 2.23/2.46 tff(12765,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(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(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12764, 12762])).
% 2.23/2.46 tff(12766,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12767,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12766, 12765])).
% 2.23/2.46 tff(12768,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12767, 245, 12761, 12683, 12384, 12759, 12743])).
% 2.23/2.46 tff(12769,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12770,plain,
% 2.23/2.46 (~r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12769, 3380, 310, 289, 11227])).
% 2.23/2.46 tff(12771,plain,
% 2.23/2.46 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[809, 12770])).
% 2.23/2.46 tff(12772,plain,
% 2.23/2.46 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12773,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12772])).
% 2.23/2.46 tff(12774,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12773, 6395])).
% 2.23/2.46 tff(12775,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12776,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12775, 12774])).
% 2.23/2.46 tff(12777,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12776, 245, 355, 2222, 709, 919])).
% 2.23/2.46 tff(12778,plain,((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12779,plain,
% 2.23/2.46 (~b(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12778, 12648, 12771, 12384])).
% 2.23/2.46 tff(12780,plain,
% 2.23/2.46 (r(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[232, 12779])).
% 2.23/2.46 tff(12781,plain,
% 2.23/2.46 (~r(s(elem!1), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[4743, 1449, 11122])).
% 2.23/2.46 tff(12782,plain,
% 2.23/2.46 (~r(elem!1, s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12505, 12781])).
% 2.23/2.46 tff(12783,plain,
% 2.23/2.46 (b(elem!1, s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10716, 12782])).
% 2.23/2.46 tff(12784,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12783, 12390])).
% 2.23/2.46 tff(12785,plain,
% 2.23/2.46 (~r(s(s(s(z))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12524, 12784, 12780, 3380, 289])).
% 2.23/2.46 tff(12786,plain,
% 2.23/2.46 (b(s(s(s(z))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[7060, 12785])).
% 2.23/2.46 tff(12787,plain,
% 2.23/2.46 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12534, 12786, 12648, 12384])).
% 2.23/2.46 tff(12788,plain,
% 2.23/2.46 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1515, 12787])).
% 2.23/2.46 tff(12789,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12790,plain,
% 2.23/2.46 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12791,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12790])).
% 2.23/2.46 tff(12792,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12791, 12789])).
% 2.23/2.46 tff(12793,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12794,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12793, 12792])).
% 2.23/2.46 tff(12795,plain,
% 2.23/2.46 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12794, 245, 12784, 3380, 12771])).
% 2.23/2.46 tff(12796,plain,
% 2.23/2.46 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12795, 12552])).
% 2.23/2.46 tff(12797,plain,
% 2.23/2.46 (r(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[11051, 12796])).
% 2.23/2.46 tff(12798,plain,
% 2.23/2.46 (~r(elem!1, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[7550, 12797, 12788])).
% 2.23/2.46 tff(12799,plain,
% 2.23/2.46 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[199])).
% 2.23/2.46 tff(12800,plain,
% 2.23/2.46 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12799])).
% 2.23/2.46 tff(12801,plain,
% 2.23/2.46 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12800])).
% 2.23/2.46 tff(12802,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.23/2.46 tff(12803,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12802, 12801])).
% 2.23/2.46 tff(12804,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[11852, 12803])).
% 2.23/2.46 tff(12805,plain,(r(elem!1, s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12806,plain,
% 2.23/2.46 (r(elem!1, s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12805, 12381])).
% 2.23/2.46 tff(12807,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12806, 12798])).
% 2.23/2.46 tff(12808,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12416, 12807])).
% 2.23/2.46 tff(12809,plain,
% 2.23/2.46 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12637, 12788, 11227])).
% 2.23/2.46 tff(12810,plain,
% 2.23/2.46 (~r(s(s(s(z))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12601, 12809])).
% 2.23/2.46 tff(12811,plain,
% 2.23/2.46 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[11873, 12810])).
% 2.23/2.46 tff(12812,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[11866, 12811])).
% 2.23/2.46 tff(12813,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12812, 12358])).
% 2.23/2.46 tff(12814,plain,
% 2.23/2.46 (~b(s(z), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12693, 245, 12813, 12784, 3380])).
% 2.23/2.46 tff(12815,plain,
% 2.23/2.46 ((s(z) = s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10887, 32, 12814])).
% 2.23/2.46 tff(12816,plain,
% 2.23/2.46 (r(s(z), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12815, 10877])).
% 2.23/2.46 tff(12817,plain,
% 2.23/2.46 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12731, 12816, 12813, 12808, 3380])).
% 2.23/2.46 tff(12818,plain,
% 2.23/2.46 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12354, 12817])).
% 2.23/2.46 tff(12819,plain,
% 2.23/2.46 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12347, 12818])).
% 2.23/2.46 tff(12820,plain,
% 2.23/2.46 (r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12326, 12819])).
% 2.23/2.46 tff(12821,plain,
% 2.23/2.46 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12738, 141, 310, 12820])).
% 2.23/2.46 tff(12822,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12742, 32, 12280, 12821])).
% 2.23/2.46 tff(12823,plain,
% 2.23/2.46 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12752, 12820, 12241])).
% 2.23/2.46 tff(12824,plain,
% 2.23/2.46 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12758, 12823])).
% 2.23/2.46 tff(12825,plain,
% 2.23/2.46 (~b(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12520, 245, 12813, 12784, 3380])).
% 2.23/2.46 tff(12826,plain,
% 2.23/2.46 (r(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12078, 12825])).
% 2.23/2.46 tff(12827,plain,
% 2.23/2.46 (~r(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12681, 12826, 1449])).
% 2.23/2.46 tff(12828,plain,
% 2.23/2.46 (b(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12579, 32, 12827, 12664])).
% 2.23/2.46 tff(12829,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12830,plain,
% 2.23/2.47 (((~b(s(s(s(z))), z)) | (~b(s(s(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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12831,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12830])).
% 2.23/2.47 tff(12832,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12831, 12829])).
% 2.23/2.47 tff(12833,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12834,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12833, 12832])).
% 2.23/2.47 tff(12835,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12834, 245, 12828, 12786, 12384, 12824, 12822])).
% 2.23/2.47 tff(12836,plain,((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(12837,plain,
% 2.23/2.47 (~r(z, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12836, 3380, 310, 11227, 289])).
% 2.23/2.47 tff(12838,plain,
% 2.23/2.47 (b(z, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1421, 12837])).
% 2.23/2.47 tff(12839,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12840,plain,
% 2.23/2.47 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12841,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12840])).
% 2.23/2.47 tff(12842,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12841, 12839])).
% 2.23/2.47 tff(12843,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12844,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12843, 12842])).
% 2.23/2.47 tff(12845,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12844, 245, 4187, 2653, 3380, 2222, 709])).
% 2.23/2.47 tff(12846,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(12847,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12846, 12838, 3380, 12648, 12771])).
% 2.23/2.47 tff(12848,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[217, 12847])).
% 2.23/2.47 tff(12849,plain,
% 2.23/2.47 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[225, 12848, 12780])).
% 2.23/2.47 tff(12850,plain,
% 2.23/2.47 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2558, 12849])).
% 2.23/2.47 tff(12851,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12852,plain,
% 2.23/2.47 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12853,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12852])).
% 2.23/2.47 tff(12854,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12853, 12851])).
% 2.23/2.47 tff(12855,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12856,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12855, 12854])).
% 2.23/2.47 tff(12857,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12856, 245, 12850, 12838, 3380, 12771, 12384])).
% 2.23/2.47 tff(12858,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(12859,plain,
% 2.23/2.47 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12858, 11227, 310, 289])).
% 2.23/2.47 tff(12860,plain,
% 2.23/2.47 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12243])).
% 2.23/2.47 tff(12861,plain,
% 2.23/2.47 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12860])).
% 2.23/2.47 tff(12862,plain,
% 2.23/2.47 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[447, 12861])).
% 2.23/2.47 tff(12863,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[5156, 12862])).
% 2.23/2.47 tff(12864,plain,((~b(s(z), elem!1)) | b(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(12865,plain,
% 2.23/2.47 (~b(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12864, 12859])).
% 2.23/2.47 tff(12866,plain,
% 2.23/2.47 (r(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10872, 12865])).
% 2.23/2.47 tff(12867,plain,
% 2.23/2.47 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11689, 12866, 289])).
% 2.23/2.47 tff(12868,plain,
% 2.23/2.47 (b(s(s(s(s(s(z))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10820, 12867])).
% 2.23/2.47 tff(12869,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12868, 12250])).
% 2.23/2.47 tff(12870,plain,(b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(12871,plain,
% 2.23/2.47 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12870, 12374, 12373])).
% 2.23/2.47 tff(12872,plain,
% 2.23/2.47 (~r(s(z), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8611, 619, 12374])).
% 2.23/2.47 tff(12873,plain,
% 2.23/2.47 (b(s(z), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[232, 12872])).
% 2.23/2.47 tff(12874,plain,
% 2.23/2.47 (~r(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11547, 12374, 619, 355])).
% 2.23/2.47 tff(12875,plain,
% 2.23/2.47 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11873, 12874])).
% 2.23/2.47 tff(12876,plain,
% 2.23/2.47 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11866, 12875])).
% 2.23/2.47 tff(12877,plain,
% 2.23/2.47 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12876, 12358])).
% 2.23/2.47 tff(12878,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12879,plain,
% 2.23/2.47 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12880,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12879])).
% 2.23/2.47 tff(12881,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12880, 12878])).
% 2.23/2.47 tff(12882,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12883,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12882, 12881])).
% 2.23/2.47 tff(12884,plain,
% 2.23/2.47 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12883, 245, 12877, 8808, 11055])).
% 2.23/2.47 tff(12885,plain,
% 2.23/2.47 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1515, 12884])).
% 2.23/2.47 tff(12886,plain,
% 2.23/2.47 ((~r(s(z), elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6420, 12232])).
% 2.23/2.47 tff(12887,plain,
% 2.23/2.47 (~r(z, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12886, 12373, 619])).
% 2.23/2.47 tff(12888,plain,
% 2.23/2.47 (b(z, s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1421, 12887])).
% 2.23/2.47 tff(12889,plain,
% 2.23/2.47 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12738, 141, 310, 12254])).
% 2.23/2.47 tff(12890,plain,
% 2.23/2.47 (b(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12742, 32, 12280, 12889])).
% 2.23/2.47 tff(12891,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12892,plain,
% 2.23/2.47 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12893,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), 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(X0, 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)))))), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12892])).
% 2.23/2.47 tff(12894,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), 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(X0, 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)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12893, 12891])).
% 2.23/2.47 tff(12895,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12896,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12895, 12894])).
% 2.23/2.47 tff(12897,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12896, 245, 355, 4187, 12309, 12890])).
% 2.23/2.47 tff(12898,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(12899,plain,
% 2.23/2.47 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12898, 12888, 12373, 12248, 355])).
% 2.23/2.47 tff(12900,plain,
% 2.23/2.47 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12326, 12899])).
% 2.23/2.47 tff(12901,plain,
% 2.23/2.47 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12347, 12900])).
% 2.23/2.47 tff(12902,plain,
% 2.23/2.47 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12354, 12901])).
% 2.23/2.47 tff(12903,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12904,plain,
% 2.23/2.47 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12905,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12904])).
% 2.23/2.47 tff(12906,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12905, 12903])).
% 2.23/2.47 tff(12907,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12908,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12907, 12906])).
% 2.23/2.47 tff(12909,plain,
% 2.23/2.47 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12908, 245, 12877, 8808, 11055, 12902])).
% 2.23/2.47 tff(12910,plain,
% 2.23/2.47 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12714, 12909])).
% 2.23/2.48 tff(12911,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12912,plain,
% 2.23/2.48 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12913,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12912])).
% 2.23/2.48 tff(12914,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[12913, 12911])).
% 2.23/2.48 tff(12915,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(12916,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12915, 12914])).
% 2.23/2.48 tff(12917,plain,
% 2.23/2.48 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12916, 245, 8808, 11055, 12902])).
% 2.23/2.48 tff(12918,plain,
% 2.23/2.48 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12757, 12917, 12284])).
% 2.23/2.48 tff(12919,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.23/2.48 tff(12920,plain,
% 2.23/2.48 (((~![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(s(z))), s(s(s(s(s(z))))))) | (~r(s(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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12921,plain,
% 2.23/2.48 (((~r(s(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(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(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12922,plain,
% 2.23/2.48 (((~![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(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))))))))) <=> ((~![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(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12921])).
% 2.23/2.48 tff(12923,plain,
% 2.23/2.48 (((~![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(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))))))))) <=> ((~![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(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[12922, 12920])).
% 2.23/2.48 tff(12924,plain,
% 2.23/2.48 ((~![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(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))))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(12925,plain,
% 2.23/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12924, 12923])).
% 2.23/2.48 tff(12926,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12925, 141, 6013, 12744, 12919])).
% 2.23/2.48 tff(12927,plain,((~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(s(s(z))))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(12928,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12927, 12918, 12910, 12885])).
% 2.23/2.48 tff(12929,plain,(b(z, elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(12930,plain,
% 2.23/2.48 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12929, 12873, 90, 12871, 619])).
% 2.23/2.48 tff(12931,plain,
% 2.23/2.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), 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(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12932,plain,
% 2.23/2.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(12933,plain,
% 2.23/2.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12932, 12931])).
% 2.23/2.48 tff(12934,plain,
% 2.23/2.48 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12933, 32, 12930, 12367])).
% 2.23/2.48 tff(12935,plain,
% 2.23/2.48 (~r(z, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12886, 619, 12373])).
% 2.23/2.48 tff(12936,plain,
% 2.23/2.48 (b(z, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1421, 12935])).
% 2.23/2.48 tff(12937,plain,
% 2.23/2.48 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12898, 12248, 12373, 12936, 12873])).
% 2.23/2.48 tff(12938,plain,
% 2.23/2.48 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12326, 12937])).
% 2.23/2.48 tff(12939,plain,
% 2.23/2.48 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12347, 12938])).
% 2.23/2.48 tff(12940,plain,
% 2.23/2.48 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12354, 12939])).
% 2.23/2.48 tff(12941,plain,
% 2.23/2.48 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12232])).
% 2.23/2.48 tff(12942,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), z) <=> b(elem!1, z)),
% 2.23/2.48 inference(symmetry,[status(thm)],[12941])).
% 2.23/2.48 tff(12943,plain,
% 2.23/2.48 ((~b(s(s(s(s(elem!1)))), z)) <=> (~b(elem!1, z))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12942])).
% 2.23/2.48 tff(12944,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.23/2.48 tff(12945,plain,
% 2.23/2.48 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11873, 11548])).
% 2.23/2.48 tff(12946,plain,
% 2.23/2.48 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11866, 12945])).
% 2.23/2.48 tff(12947,plain,
% 2.23/2.48 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12946, 12358])).
% 2.23/2.48 tff(12948,plain,
% 2.23/2.48 (r(s(s(s(s(elem!1)))), z) <=> r(elem!1, z)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12243])).
% 2.23/2.48 tff(12949,plain,
% 2.23/2.48 (r(elem!1, z)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[106, 12948])).
% 2.23/2.48 tff(12950,plain,
% 2.23/2.48 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[731, 12949, 722])).
% 2.23/2.48 tff(12951,plain,
% 2.23/2.48 (b(elem!1, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11051, 12950])).
% 2.23/2.48 tff(12952,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12951, 12235])).
% 2.23/2.48 tff(12953,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11232, 106, 722])).
% 2.23/2.48 tff(12954,plain,
% 2.23/2.48 (~r(s(s(s(elem!1))), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[2109, 12180, 220])).
% 2.23/2.48 tff(12955,plain,
% 2.23/2.48 (~r(elem!1, z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11676, 12954])).
% 2.23/2.48 tff(12956,plain,
% 2.23/2.48 (b(elem!1, z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10943, 12955])).
% 2.23/2.48 tff(12957,plain,
% 2.23/2.48 (~r(z, elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[8611, 619, 220])).
% 2.23/2.48 tff(12958,plain,
% 2.23/2.48 (b(z, elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10913, 12957])).
% 2.23/2.48 tff(12959,plain,
% 2.23/2.48 (~r(s(s(s(s(s(z))))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[7135, 141, 220, 722])).
% 2.23/2.48 tff(12960,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[809, 12959])).
% 2.23/2.48 tff(12961,plain,
% 2.23/2.48 (~r(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[8430, 980, 619])).
% 2.23/2.48 tff(12962,plain,
% 2.23/2.48 (b(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10863, 12961])).
% 2.23/2.48 tff(12963,plain,
% 2.23/2.48 (~r(s(s(s(z))), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[985, 980, 220])).
% 2.23/2.48 tff(12964,plain,
% 2.23/2.48 (b(s(s(s(z))), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[7060, 12963])).
% 2.23/2.48 tff(12965,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11969, 12964, 12962, 12958, 12956])).
% 2.23/2.48 tff(12966,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(12967,plain,
% 2.23/2.48 (~r(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12966, 619, 220])).
% 2.23/2.48 tff(12968,plain,
% 2.23/2.48 (b(s(s(s(z))), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12078, 12967])).
% 2.23/2.48 tff(12969,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[6239, 245, 6306, 6123, 709, 8565])).
% 2.23/2.48 tff(12970,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(12971,plain,
% 2.23/2.48 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12970, 12968, 12960, 9269])).
% 2.23/2.48 tff(12972,plain,
% 2.23/2.48 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1515, 12971])).
% 2.23/2.48 tff(12973,plain,
% 2.23/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12974,plain,
% 2.23/2.48 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12975,plain,
% 2.23/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12974])).
% 2.23/2.48 tff(12976,plain,
% 2.23/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[12975, 12973])).
% 2.23/2.48 tff(12977,plain,
% 2.23/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(12978,plain,
% 2.23/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12977, 12976])).
% 2.23/2.48 tff(12979,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12978, 141, 6013, 722, 979])).
% 2.23/2.48 tff(12980,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(12981,plain,
% 2.23/2.48 (~r(s(s(s(z))), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12980, 12972, 722])).
% 2.23/2.48 tff(12982,plain,
% 2.23/2.48 (b(s(s(s(z))), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[7060, 12981])).
% 2.23/2.48 tff(12983,plain,
% 2.23/2.48 (~b(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[11969, 12982, 12958, 12956])).
% 2.23/2.48 tff(12984,plain,
% 2.23/2.48 (r(s(s(s(z))), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10863, 12983])).
% 2.23/2.48 tff(12985,plain,
% 2.23/2.48 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12601, 12984])).
% 2.23/2.48 tff(12986,plain,
% 2.23/2.48 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12359, 12984, 9269, 619])).
% 2.23/2.48 tff(12987,plain,
% 2.23/2.48 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10773, 12986])).
% 2.23/2.48 tff(12988,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10793, 12987])).
% 2.23/2.48 tff(12989,plain,
% 2.23/2.48 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12988, 10663])).
% 2.23/2.48 tff(12990,plain,
% 2.23/2.48 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12956, 12941])).
% 2.23/2.48 tff(12991,plain,
% 2.23/2.48 ((~b(z, elem!1)) | b(z, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[4808, 12232])).
% 2.23/2.48 tff(12992,plain,
% 2.23/2.48 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12991, 12958])).
% 2.23/2.48 tff(12993,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12994,plain,
% 2.23/2.48 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(12995,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[12994])).
% 2.23/2.48 tff(12996,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[12995, 12993])).
% 2.23/2.48 tff(12997,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(12998,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12997, 12996])).
% 2.23/2.48 tff(12999,plain,
% 2.23/2.48 (~b(z, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12998, 245, 12992, 12990, 12989])).
% 2.23/2.48 tff(13000,plain,
% 2.23/2.48 (r(z, s(s(s(s(s(z))))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[758, 12999])).
% 2.23/2.48 tff(13001,plain,
% 2.23/2.48 (((~![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(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(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13002,plain,
% 2.23/2.48 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13003,plain,
% 2.23/2.48 (((~![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(z, 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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[13002])).
% 2.23/2.48 tff(13004,plain,
% 2.23/2.48 (((~![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(z, 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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[13003, 13001])).
% 2.23/2.48 tff(13005,plain,
% 2.23/2.48 ((~![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(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(13006,plain,
% 2.23/2.48 ((~![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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[13005, 13004])).
% 2.23/2.48 tff(13007,plain,
% 2.23/2.48 (~r(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[13006, 141, 12972, 13000])).
% 2.23/2.48 tff(13008,plain,
% 2.23/2.48 (b(z, s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[12579, 32, 13007, 12664])).
% 2.23/2.48 tff(13009,plain,
% 2.23/2.48 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.23/2.48 inference(commutativity,[status(thm)],[])).
% 2.23/2.48 tff(13010,plain,
% 2.23/2.48 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.23/2.48 inference(symmetry,[status(thm)],[13009])).
% 2.23/2.48 tff(13011,plain,
% 2.23/2.48 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[13010])).
% 2.23/2.48 tff(13012,plain,
% 2.23/2.48 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[12282, 13011])).
% 2.23/2.48 tff(13013,plain,
% 2.23/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(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(elem!1)))))) | (~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(z))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13014,plain,
% 2.23/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(z))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(13015,plain,
% 2.23/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(z)))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[13014, 13013])).
% 2.23/2.48 tff(13016,plain,
% 2.23/2.48 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[13015, 141, 12568, 12254])).
% 2.23/2.48 tff(13017,plain,
% 2.23/2.48 (((~![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)))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13018,plain,
% 2.23/2.48 ((~![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)))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(13019,plain,
% 2.23/2.48 ((~![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))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[13018, 13017])).
% 2.23/2.48 tff(13020,plain,
% 2.23/2.48 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[13019, 32, 13016])).
% 2.23/2.48 tff(13021,plain,
% 2.23/2.48 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[13020, 13012])).
% 2.23/2.48 tff(13022,plain,
% 2.23/2.48 (((~![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(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13023,plain,
% 2.23/2.48 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13024,plain,
% 2.23/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(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(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[13023])).
% 2.23/2.48 tff(13025,plain,
% 2.23/2.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(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(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[13024, 13022])).
% 2.23/2.48 tff(13026,plain,
% 2.23/2.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(13027,plain,
% 2.23/2.48 ((~![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(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[13026, 13025])).
% 2.23/2.48 tff(13028,plain,
% 2.23/2.48 (~r(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[13027, 141, 12568, 12290])).
% 2.23/2.48 tff(13029,plain,
% 2.23/2.48 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10887, 32, 13028])).
% 2.23/2.48 tff(13030,plain,
% 2.23/2.48 (b(s(z), s(s(s(z))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[13029, 10877])).
% 2.23/2.48 tff(13031,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 2.23/2.48 tff(13032,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(X0, 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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13033,plain,
% 2.23/2.48 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(13034,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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(X0, 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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[13033])).
% 2.23/2.49 tff(13035,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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(X0, 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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[13034, 13032])).
% 2.23/2.49 tff(13036,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), 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)))))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(13037,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13036, 13035])).
% 2.23/2.49 tff(13038,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13037, 245, 13031, 911, 12309, 13030, 13021])).
% 2.23/2.49 tff(13039,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(13040,plain,
% 2.23/2.49 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13039, 13008, 12982, 12248, 12985])).
% 2.23/2.49 tff(13041,plain,
% 2.23/2.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13042,plain,
% 2.23/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(13043,plain,
% 2.23/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13042, 13041])).
% 2.23/2.49 tff(13044,plain,
% 2.23/2.49 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13043, 32, 13040, 12341])).
% 2.23/2.49 tff(13045,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(s(s(s(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(X0, 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(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13046,plain,
% 2.23/2.49 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13047,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(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(X0, 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(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[13046])).
% 2.23/2.49 tff(13048,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(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(X0, 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(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[13047, 13045])).
% 2.23/2.49 tff(13049,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(13050,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13049, 13048])).
% 2.23/2.49 tff(13051,plain,
% 2.23/2.49 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13050, 245, 12992, 12990, 13044])).
% 2.23/2.49 tff(13052,plain,
% 2.23/2.49 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 2.23/2.49 inference(commutativity,[status(thm)],[])).
% 2.23/2.49 tff(13053,plain,
% 2.23/2.49 ((s(s(s(s(s(s(z)))))) = z) <=> (z = s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(symmetry,[status(thm)],[13052])).
% 2.23/2.49 tff(13054,plain,
% 2.23/2.49 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = s(s(s(s(s(s(z))))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[13053])).
% 2.23/2.49 tff(13055,plain,
% 2.23/2.49 (~(z = s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[12280, 13054])).
% 2.23/2.49 tff(13056,plain,
% 2.23/2.49 (((~![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))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13057,plain,
% 2.23/2.49 ((~![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))))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(13058,plain,
% 2.23/2.49 ((~![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)))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13057, 13056])).
% 2.23/2.49 tff(13059,plain,
% 2.23/2.49 ((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)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13058, 32])).
% 2.23/2.49 tff(13060,plain,
% 2.23/2.49 (b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13059, 13055])).
% 2.23/2.49 tff(13061,plain,
% 2.23/2.49 (r(z, s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13060, 13051])).
% 2.23/2.49 tff(13062,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13063,plain,
% 2.23/2.49 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13064,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[13063])).
% 2.23/2.49 tff(13065,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[13064, 13062])).
% 2.23/2.49 tff(13066,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(13067,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13066, 13065])).
% 2.23/2.49 tff(13068,plain,
% 2.23/2.49 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13067, 245, 12992, 12990, 12989, 13044])).
% 2.23/2.49 tff(13069,plain,
% 2.23/2.49 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12757, 13068, 12284])).
% 2.23/2.49 tff(13070,plain,
% 2.23/2.49 (((~![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(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(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13071,plain,
% 2.23/2.49 (((~r(s(s(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(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13072,plain,
% 2.23/2.49 (((~![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(s(s(z)))))))) | (~r(z, s(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(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[13071])).
% 2.23/2.49 tff(13073,plain,
% 2.23/2.49 (((~![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(s(s(z)))))))) | (~r(z, s(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(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[13072, 13070])).
% 2.23/2.49 tff(13074,plain,
% 2.23/2.49 ((~![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(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(13075,plain,
% 2.23/2.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13074, 13073])).
% 2.23/2.49 tff(13076,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13075, 141, 13000, 13069, 13061])).
% 2.23/2.49 tff(13077,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(13078,plain,
% 2.23/2.49 (~r(s(z), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13077, 220, 722])).
% 2.23/2.49 tff(13079,plain,
% 2.23/2.49 (b(s(z), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10872, 13078])).
% 2.23/2.49 tff(13080,plain,
% 2.23/2.49 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12864, 13079])).
% 2.23/2.49 tff(13081,plain,
% 2.23/2.49 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[225, 106, 220])).
% 2.23/2.49 tff(13082,plain,
% 2.23/2.49 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12438, 12953, 13080, 12960])).
% 2.23/2.49 tff(13083,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[217, 13082, 13081])).
% 2.23/2.49 tff(13084,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(13085,plain,
% 2.23/2.49 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13084, 220, 722])).
% 2.23/2.49 tff(13086,plain,
% 2.23/2.49 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2558, 13085])).
% 2.23/2.49 tff(13087,plain,
% 2.23/2.49 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12382, 12380, 722])).
% 2.23/2.49 tff(13088,plain,
% 2.23/2.49 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10793, 13087])).
% 2.23/2.49 tff(13089,plain,
% 2.23/2.49 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13088, 10663])).
% 2.23/2.49 tff(13090,plain,
% 2.23/2.49 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12478, 13089, 220, 13080, 11122])).
% 2.23/2.49 tff(13091,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[2558, 13090])).
% 2.23/2.49 tff(13092,plain,
% 2.23/2.49 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12438, 13089, 13080, 12960])).
% 2.23/2.49 tff(13093,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[217, 13092])).
% 2.23/2.49 tff(13094,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[225, 13093, 13091, 220])).
% 2.23/2.49 tff(13095,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(13096,plain,
% 2.23/2.49 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13095, 220, 722])).
% 2.23/2.49 tff(13097,plain,
% 2.23/2.49 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1992, 13096])).
% 2.23/2.49 tff(13098,plain,
% 2.23/2.49 (b(z, elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12371, 13097])).
% 2.23/2.49 tff(13099,plain,
% 2.23/2.49 ((~b(s(s(s(s(elem!1)))), z)) | b(elem!1, z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1949, 12381])).
% 2.23/2.49 tff(13100,plain,
% 2.23/2.49 (b(elem!1, z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13099, 13086])).
% 2.23/2.49 tff(13101,plain,
% 2.23/2.49 (~b(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[4595, 13100, 13079, 13098])).
% 2.23/2.49 tff(13102,plain,
% 2.23/2.49 (r(z, s(z))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1421, 13101])).
% 2.23/2.49 tff(13103,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~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(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13104,plain,
% 2.23/2.49 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(13105,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[13104])).
% 2.23/2.49 tff(13106,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[13105, 13103])).
% 2.23/2.49 tff(13107,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(13108,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[13107, 13106])).
% 2.23/2.49 tff(13109,plain,
% 2.23/2.49 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13108, 245, 2197, 1943, 3380, 12699])).
% 2.23/2.49 tff(13110,plain,
% 2.23/2.49 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[12308, 13109])).
% 2.23/2.49 tff(13111,plain,
% 2.23/2.49 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[13050, 245, 2197, 1943, 12699])).
% 2.23/2.49 tff(13112,plain,
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[13060, 13111])).
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% 2.23/2.49 inference(rewrite,[status(thm)],[])).
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% 2.23/2.49 inference(rewrite,[status(thm)],[])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[12354, 13121])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[12347, 13122])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[12326, 13123])).
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% 2.23/2.49 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[12232])).
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% 2.23/2.49 inference(unit_resolution,[status(thm)],[7284, 13100, 13079, 13098])).
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% 2.23/2.50 inference(unit_resolution,[status(thm)],[10820, 13126])).
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% 2.23/2.50 inference(unit_resolution,[status(thm)],[12601, 13132])).
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% 2.23/2.50 inference(rewrite,[status(thm)],[])).
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% 2.23/2.50 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.50 inference(rewrite,[status(thm)],[])).
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% 2.23/2.50 (((~![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(elem!1)))))) | (~r(s(s(s(z))), s(s(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(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.23/2.50 inference(monotonicity,[status(thm)],[13135])).
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% 2.23/2.50 (((~![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(elem!1)))))) | (~r(s(s(s(z))), s(s(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(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.23/2.50 inference(transitivity,[status(thm)],[13136, 13134])).
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% 2.23/2.50 inference(quant_inst,[status(thm)],[])).
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% 2.23/2.50 inference(modus_ponens,[status(thm)],[13138, 13137])).
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% 2.23/2.50 inference(unit_resolution,[status(thm)],[13139, 141, 13133, 13124])).
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% 2.23/2.50 inference(unit_resolution,[status(thm)],[12714, 13140])).
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% 2.33/2.50 inference(modus_ponens,[status(thm)],[13143, 13142])).
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% 2.33/2.50 tff(13147,plain,
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% 2.33/2.50 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
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% 2.33/2.50 (b(s(s(s(z))), s(s(s(s(s(z))))))),
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% 2.33/2.50 tff(13151,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
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% 2.33/2.50 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
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% 2.33/2.50 tff(13155,plain,
% 2.33/2.50 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12416, 13154])).
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% 2.33/2.50 (r(elem!1, s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12806, 13155])).
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% 2.33/2.50 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
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% 2.33/2.50 inference(monotonicity,[status(thm)],[13157])).
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% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
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% 2.33/2.50 inference(modus_ponens,[status(thm)],[13160, 13159])).
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% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13161, 245, 3380, 6306, 709, 11055])).
% 2.33/2.50 tff(13163,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(13164,plain,
% 2.33/2.50 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13163, 13080, 9269, 12960])).
% 2.33/2.50 tff(13165,plain,
% 2.33/2.50 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[13164, 12552])).
% 2.33/2.50 tff(13166,plain,
% 2.33/2.50 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11051, 13165])).
% 2.33/2.50 tff(13167,plain,
% 2.33/2.50 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[7550, 13166, 13156])).
% 2.33/2.50 tff(13168,plain,
% 2.33/2.50 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1515, 13167])).
% 2.33/2.50 tff(13169,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(13170,plain,
% 2.33/2.50 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(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(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(13171,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[13170])).
% 2.33/2.50 tff(13172,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[13171, 13169])).
% 2.33/2.50 tff(13173,plain,
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% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(13174,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[13173, 13172])).
% 2.33/2.50 tff(13175,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13174, 245, 13153, 13168, 13146, 13141, 13130])).
% 2.33/2.50 tff(13176,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(13177,plain,
% 2.33/2.50 (~r(s(z), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13176, 722])).
% 2.33/2.50 tff(13178,plain,
% 2.33/2.50 (b(s(z), z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[232, 13177])).
% 2.33/2.50 tff(13179,plain,
% 2.33/2.50 (b(z, elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12929, 12953, 12952, 13178, 619])).
% 2.33/2.50 tff(13180,plain,
% 2.33/2.50 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12991, 13179])).
% 2.33/2.50 tff(13181,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(13182,plain,
% 2.33/2.50 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(13183,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[13182])).
% 2.33/2.50 tff(13184,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[13183, 13181])).
% 2.33/2.50 tff(13185,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
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% 2.33/2.50 inference(modus_ponens,[status(thm)],[13185, 13184])).
% 2.33/2.50 tff(13187,plain,
% 2.33/2.50 (~b(z, s(s(s(s(s(z))))))),
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% 2.33/2.50 tff(13188,plain,
% 2.33/2.50 (r(z, s(s(s(s(s(z))))))),
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% 2.33/2.50 tff(13189,plain,
% 2.33/2.50 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[6809, 12949, 722])).
% 2.33/2.50 tff(13190,plain,
% 2.33/2.50 (b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10820, 13189])).
% 2.33/2.50 tff(13191,plain,
% 2.33/2.50 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[5823, 12235])).
% 2.33/2.50 tff(13192,plain,
% 2.33/2.50 (b(z, elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12929, 8808, 13191, 355, 619])).
% 2.33/2.50 tff(13193,plain,
% 2.33/2.50 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12991, 13192])).
% 2.33/2.50 tff(13194,plain,
% 2.33/2.50 (~b(z, s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13186, 245, 13193, 8808, 13191])).
% 2.33/2.50 tff(13195,plain,
% 2.33/2.50 (r(z, s(s(s(s(s(z))))))),
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% 2.33/2.50 tff(13196,plain,
% 2.33/2.50 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[6319, 10862])).
% 2.33/2.50 tff(13197,plain,
% 2.33/2.50 (~b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13196, 6123, 5823, 4878, 619])).
% 2.33/2.50 tff(13198,plain,
% 2.33/2.50 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1698, 13197])).
% 2.33/2.50 tff(13199,plain,
% 2.33/2.50 (~r(z, s(z))),
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% 2.33/2.50 tff(13200,plain,
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% 2.33/2.50 inference(unit_resolution,[status(thm)],[1421, 13199])).
% 2.33/2.50 tff(13201,plain,
% 2.33/2.50 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11078, 6123, 4878, 5823, 13191])).
% 2.33/2.50 tff(13202,plain,
% 2.33/2.50 (~b(s(elem!1), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11068, 13201])).
% 2.33/2.50 tff(13203,plain,
% 2.33/2.50 (r(s(elem!1), s(s(s(z))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11061, 13202])).
% 2.33/2.50 tff(13204,plain,
% 2.33/2.50 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(elem!1))),
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% 2.33/2.50 tff(13205,plain,
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% 2.33/2.50 (~b(s(elem!1), s(z))),
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% 2.33/2.50 tff(13207,plain,
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% 2.33/2.50 tff(13208,plain,
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% 2.33/2.50 tff(13209,plain,
% 2.33/2.50 (b(s(s(s(z))), s(z))),
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% 2.33/2.50 tff(13210,plain,
% 2.33/2.50 (~b(s(s(s(z))), z)),
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% 2.33/2.50 tff(13211,plain,
% 2.33/2.50 (r(s(s(s(z))), z)),
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% 2.33/2.50 tff(13212,plain,
% 2.33/2.50 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(symmetry,[status(thm)],[12356])).
% 2.33/2.50 tff(13213,plain,
% 2.33/2.50 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), elem!1))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[13212])).
% 2.33/2.50 tff(13214,plain,
% 2.33/2.50 (((~b(s(s(s(s(elem!1)))), s(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1))))))) <=> ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(13215,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[13214])).
% 2.33/2.50 tff(13216,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[13215, 12878])).
% 2.33/2.50 tff(13217,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(13218,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[13217, 13216])).
% 2.33/2.50 tff(13219,plain,
% 2.33/2.50 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13218, 245, 6123, 8808, 13191])).
% 2.33/2.50 tff(13220,plain,
% 2.33/2.50 (~b(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[13219, 13213])).
% 2.33/2.50 tff(13221,plain,
% 2.33/2.50 (r(s(s(s(z))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10863, 13220])).
% 2.33/2.50 tff(13222,plain,
% 2.33/2.50 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[12601, 13221])).
% 2.33/2.50 tff(13223,plain,
% 2.33/2.50 (((~![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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(13224,plain,
% 2.33/2.50 ((~![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(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(13225,plain,
% 2.33/2.50 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[13224, 13223])).
% 2.33/2.50 tff(13226,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[13225, 141, 106, 13222, 13211])).
% 2.33/2.51 tff(13227,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13228,plain,
% 2.33/2.51 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13227, 106, 13178, 12953, 13190, 12951, 619])).
% 2.33/2.51 tff(13229,plain,
% 2.33/2.51 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1515, 13228])).
% 2.33/2.51 tff(13230,plain,
% 2.33/2.51 (~r(s(s(s(z))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12980, 13229, 722])).
% 2.33/2.51 tff(13231,plain,
% 2.33/2.51 (b(s(s(s(z))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[7060, 13230])).
% 2.33/2.51 tff(13232,plain,
% 2.33/2.51 (~r(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12386, 13229, 997])).
% 2.33/2.51 tff(13233,plain,
% 2.33/2.51 (b(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12078, 13232])).
% 2.33/2.51 tff(13234,plain,
% 2.33/2.51 (~b(z, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8573, 13233, 13178, 13231])).
% 2.33/2.51 tff(13235,plain,
% 2.33/2.51 (r(z, s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1421, 13234])).
% 2.33/2.51 tff(13236,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11139, 141, 13235, 13188, 997])).
% 2.33/2.51 tff(13237,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13238,plain,
% 2.33/2.51 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13237, 106, 619, 722])).
% 2.33/2.51 tff(13239,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[809, 13238])).
% 2.33/2.51 tff(13240,plain,
% 2.33/2.51 (~b(z, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[6331, 245, 355, 4187, 13239])).
% 2.33/2.51 tff(13241,plain,
% 2.33/2.51 (r(z, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[758, 13240])).
% 2.33/2.51 tff(13242,plain,
% 2.33/2.51 (~b(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12101, 13241, 355, 4187, 13239])).
% 2.33/2.51 tff(13243,plain,
% 2.33/2.51 (r(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12078, 13242])).
% 2.33/2.51 tff(13244,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11857, 13243, 219])).
% 2.33/2.51 tff(13245,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[8808, 12237])).
% 2.33/2.51 tff(13246,plain,
% 2.33/2.51 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13227, 12951, 8808, 355, 13245, 106, 619])).
% 2.33/2.51 tff(13247,plain,
% 2.33/2.51 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1515, 13246])).
% 2.33/2.51 tff(13248,assumption,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.33/2.51 tff(13249,plain,
% 2.33/2.51 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12706, 245, 12698, 11070])).
% 2.33/2.51 tff(13250,plain,
% 2.33/2.51 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13249, 12699])).
% 2.33/2.51 tff(13251,plain,
% 2.33/2.51 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12713, 13250, 13248])).
% 2.33/2.51 tff(13252,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.33/2.51 tff(13253,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13254,plain,
% 2.33/2.51 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13255,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[13254])).
% 2.33/2.51 tff(13256,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[13255, 13253])).
% 2.33/2.51 tff(13257,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(13258,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[13257, 13256])).
% 2.33/2.51 tff(13259,plain,
% 2.33/2.51 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13258, 245, 12698, 11070, 8808])).
% 2.33/2.51 tff(13260,plain,
% 2.33/2.51 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13259, 12699])).
% 2.33/2.51 tff(13261,plain,
% 2.33/2.51 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12757, 13260, 13252])).
% 2.33/2.51 tff(13262,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12925, 141, 6013, 13261, 13251])).
% 2.33/2.51 tff(13263,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13264,plain,
% 2.33/2.51 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13263, 12282])).
% 2.33/2.51 tff(13265,plain,
% 2.33/2.51 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13264, 12284])).
% 2.33/2.51 tff(13266,plain,
% 2.33/2.51 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13265, 13247, 8808, 12699, 12698])).
% 2.33/2.51 tff(13267,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12416, 13266, 13244])).
% 2.33/2.51 tff(13268,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13269,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13268, 219, 12699, 12947, 8808, 11536, 619, 4187, 722])).
% 2.33/2.51 tff(13270,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2558, 13269])).
% 2.33/2.51 tff(13271,plain,
% 2.33/2.51 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[12944, 12552])).
% 2.33/2.51 tff(13272,plain,
% 2.33/2.51 (r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11051, 13271])).
% 2.33/2.51 tff(13273,plain,
% 2.33/2.51 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[748, 13272, 289])).
% 2.33/2.51 tff(13274,plain,
% 2.33/2.51 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[758, 13273])).
% 2.33/2.51 tff(13275,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(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(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13276,plain,
% 2.33/2.51 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13277,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[13276])).
% 2.33/2.51 tff(13278,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[13277, 13275])).
% 2.33/2.51 tff(13279,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(13280,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[13279, 13278])).
% 2.33/2.51 tff(13281,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13280, 245, 1943, 12698, 6123, 13274, 8808])).
% 2.33/2.51 tff(13282,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13283,plain,
% 2.33/2.51 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13282, 13270, 12947, 8808, 289, 12944])).
% 2.33/2.51 tff(13284,plain,
% 2.33/2.51 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1515, 13283])).
% 2.33/2.51 tff(13285,plain,
% 2.33/2.51 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13265, 13284, 8808, 12699, 12947])).
% 2.33/2.51 tff(13286,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12416, 13285])).
% 2.33/2.51 tff(13287,plain,
% 2.33/2.51 (~r(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11857, 13286, 219])).
% 2.33/2.51 tff(13288,plain,
% 2.33/2.51 (~r(s(s(s(z))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12980, 13284, 722])).
% 2.33/2.51 tff(13289,plain,
% 2.33/2.51 (b(s(s(s(z))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[7060, 13288])).
% 2.33/2.51 tff(13290,plain,
% 2.33/2.51 (~b(s(s(s(z))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[8573, 13289, 11536, 4187])).
% 2.33/2.51 tff(13291,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12078, 13290, 13287])).
% 2.33/2.51 tff(13292,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13293,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13292, 722, 4187, 8808, 12699, 289, 12944, 619])).
% 2.33/2.51 tff(13294,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[217, 13293])).
% 2.33/2.51 tff(13295,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13296,plain,
% 2.33/2.51 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13297,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[13296])).
% 2.33/2.51 tff(13298,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[13297, 13295])).
% 2.33/2.51 tff(13299,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(13300,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[13299, 13298])).
% 2.33/2.51 tff(13301,plain,
% 2.33/2.51 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13300, 245, 11536, 4187, 13294])).
% 2.33/2.51 tff(13302,plain,
% 2.33/2.51 (~b(elem!1, z)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[13301, 12943])).
% 2.33/2.51 tff(13303,plain,
% 2.33/2.51 (~r(elem!1, z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[731, 13272, 722])).
% 2.33/2.51 tff(13304,plain,
% 2.33/2.51 (b(elem!1, z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10943, 13303])).
% 2.33/2.51 tff(13305,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13304, 13302])).
% 2.33/2.51 tff(13306,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13307,plain,
% 2.33/2.51 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13306, 12936, 12930, 12871, 12940, 12374, 619])).
% 2.33/2.51 tff(13308,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[738, 13307])).
% 2.33/2.51 tff(13309,plain,
% 2.33/2.51 (~b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[5992, 245, 12873, 12936, 13308])).
% 2.33/2.51 tff(13310,plain,
% 2.33/2.51 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1698, 13309])).
% 2.33/2.51 tff(13311,plain,
% 2.33/2.51 (((~![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(elem!1)))), s(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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13312,plain,
% 2.33/2.51 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13313,plain,
% 2.33/2.51 (((~![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(s(s(z))))))) | (~r(s(z), s(s(s(s(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[13312])).
% 2.33/2.51 tff(13314,plain,
% 2.33/2.51 (((~![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(s(s(z))))))) | (~r(s(z), s(s(s(s(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[13313, 13311])).
% 2.33/2.51 tff(13315,plain,
% 2.33/2.51 ((~![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(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(13316,plain,
% 2.33/2.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[13315, 13314])).
% 2.33/2.51 tff(13317,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13316, 141, 13310, 12248, 12934])).
% 2.33/2.51 tff(13318,plain,((~r(s(z), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13319,plain,
% 2.33/2.51 (~r(s(z), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13318, 90])).
% 2.33/2.51 tff(13320,plain,
% 2.33/2.51 (b(s(z), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10872, 13319])).
% 2.33/2.51 tff(13321,plain,
% 2.33/2.51 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12864, 13320])).
% 2.33/2.51 tff(13322,plain,
% 2.33/2.51 (r(z, s(elem!1))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[12373, 11121])).
% 2.33/2.51 tff(13323,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12870, 289, 310])).
% 2.33/2.51 tff(13324,plain,
% 2.33/2.51 (b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[13323, 12237])).
% 2.33/2.51 tff(13325,plain,
% 2.33/2.51 (~b(s(s(s(z))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10905, 301, 13324, 447])).
% 2.33/2.51 tff(13326,plain,
% 2.33/2.51 (r(s(s(s(z))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10863, 13325])).
% 2.33/2.51 tff(13327,plain,
% 2.33/2.51 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12601, 13326])).
% 2.33/2.51 tff(13328,plain,
% 2.33/2.51 (~r(s(s(s(z))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10163, 13326, 289])).
% 2.33/2.51 tff(13329,plain,
% 2.33/2.51 (b(s(s(s(z))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[7060, 13328])).
% 2.33/2.51 tff(13330,plain,
% 2.33/2.51 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13139, 141, 12568, 12254])).
% 2.33/2.51 tff(13331,plain,
% 2.33/2.51 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12714, 13330])).
% 2.33/2.51 tff(13332,plain,
% 2.33/2.51 (~r(z, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12574, 141, 310, 12568])).
% 2.33/2.51 tff(13333,plain,
% 2.33/2.51 (b(z, s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12579, 32, 13332, 12664])).
% 2.33/2.51 tff(13334,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13335,plain,
% 2.33/2.51 (((~b(s(s(s(z))), z)) | (~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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13336,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, 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(X0, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[13335])).
% 2.33/2.51 tff(13337,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, 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(X0, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[13336, 13334])).
% 2.33/2.51 tff(13338,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, 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)))))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(13339,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[13338, 13337])).
% 2.33/2.51 tff(13340,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13339, 245, 13333, 911, 13331, 12890])).
% 2.33/2.51 tff(13341,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(13342,plain,
% 2.33/2.51 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[13341, 13329, 13327, 310])).
% 2.33/2.51 tff(13343,plain,
% 2.33/2.51 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12326, 13342])).
% 2.33/2.51 tff(13344,plain,
% 2.33/2.51 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12347, 13343])).
% 2.33/2.51 tff(13345,plain,
% 2.33/2.51 (b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12354, 13344])).
% 2.33/2.51 tff(13346,plain,
% 2.33/2.51 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[12864, 447])).
% 2.33/2.51 tff(13347,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[301, 12390])).
% 2.33/2.51 tff(13348,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~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(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13349,plain,
% 2.33/2.51 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(13350,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[13349])).
% 2.33/2.52 tff(13351,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(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(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[13350, 13348])).
% 2.33/2.52 tff(13352,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(13353,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[13352, 13351])).
% 2.33/2.52 tff(13354,plain,
% 2.33/2.52 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13353, 245, 13347, 13346, 13345])).
% 2.33/2.52 tff(13355,plain,
% 2.33/2.52 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12308, 13354])).
% 2.33/2.52 tff(13356,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13357,plain,
% 2.33/2.52 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13358,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[13357])).
% 2.33/2.52 tff(13359,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[13358, 13356])).
% 2.33/2.52 tff(13360,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(13361,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[13360, 13359])).
% 2.33/2.52 tff(13362,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13361, 245, 13347, 13346, 13323, 13345])).
% 2.33/2.52 tff(13363,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12758, 13362])).
% 2.33/2.52 tff(13364,plain,
% 2.33/2.52 (~b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11043, 245, 13347, 13346, 13323])).
% 2.33/2.52 tff(13365,plain,
% 2.33/2.52 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1698, 13364])).
% 2.33/2.52 tff(13366,plain,
% 2.33/2.52 (((~![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(s(s(s(z))))))) | (~r(s(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(z), s(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(s(s(z)))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13367,plain,
% 2.33/2.52 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13368,plain,
% 2.33/2.52 (((~![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(s(s(s(z)))))))) | (~r(s(z), s(s(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(s(z)))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[13367])).
% 2.33/2.52 tff(13369,plain,
% 2.33/2.52 (((~![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(s(s(s(z)))))))) | (~r(s(z), s(s(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(s(z)))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[13368, 13366])).
% 2.33/2.52 tff(13370,plain,
% 2.33/2.52 ((~![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(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(13371,plain,
% 2.33/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[13370, 13369])).
% 2.33/2.52 tff(13372,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13371, 141, 13365, 13363, 13355])).
% 2.33/2.52 tff(13373,plain,((~b(elem!1, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(13374,plain,
% 2.33/2.52 (~b(elem!1, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13373, 12373, 12374, 13320])).
% 2.33/2.52 tff(13375,plain,
% 2.33/2.52 (r(elem!1, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10716, 13374])).
% 2.33/2.52 tff(13376,plain,
% 2.33/2.52 ((~r(elem!1, s(z))) | r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4612, 12232])).
% 2.33/2.52 tff(13377,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13376, 13375])).
% 2.33/2.52 tff(13378,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12478, 220, 1342, 8808, 3380])).
% 2.33/2.52 tff(13379,plain,
% 2.33/2.52 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[225, 220, 219])).
% 2.33/2.52 tff(13380,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2558, 13379, 13378])).
% 2.33/2.52 tff(13381,plain,((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(13382,plain,
% 2.33/2.52 (~r(s(z), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13381, 13377, 13322, 12871, 13321])).
% 2.33/2.52 tff(13383,plain,
% 2.33/2.52 (b(s(z), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[232, 13382])).
% 2.33/2.52 tff(13384,plain,
% 2.33/2.52 (r(s(elem!1), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12505, 13375])).
% 2.33/2.52 tff(13385,plain,
% 2.33/2.52 (~r(z, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4743, 13384, 13322])).
% 2.33/2.52 tff(13386,plain,
% 2.33/2.52 (b(z, s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1421, 13385])).
% 2.33/2.52 tff(13387,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12412, 13383, 13321, 13386])).
% 2.33/2.52 tff(13388,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2558, 13387])).
% 2.33/2.52 tff(13389,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12416, 11951])).
% 2.33/2.52 tff(13390,plain,
% 2.33/2.52 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[12513, 12358])).
% 2.33/2.52 tff(13391,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13392,plain,
% 2.33/2.52 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13393,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[13392])).
% 2.33/2.52 tff(13394,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[13393, 13391])).
% 2.33/2.52 tff(13395,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(13396,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[13395, 13394])).
% 2.33/2.52 tff(13397,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13396, 245, 13390, 13389, 3380, 8808])).
% 2.33/2.52 tff(13398,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[809, 13397])).
% 2.33/2.52 tff(13399,plain,
% 2.33/2.52 (~b(s(s(s(z))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12611, 245, 13390, 13389, 3380])).
% 2.33/2.52 tff(13400,plain,
% 2.33/2.52 (r(s(s(s(z))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12078, 13399])).
% 2.33/2.52 tff(13401,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13402,plain,
% 2.33/2.52 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13403,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[13402])).
% 2.33/2.52 tff(13404,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[13403, 13401])).
% 2.33/2.52 tff(13405,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(13406,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[13405, 13404])).
% 2.33/2.52 tff(13407,plain,
% 2.33/2.52 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13406, 245, 13390, 13389, 8808])).
% 2.33/2.52 tff(13408,plain,
% 2.33/2.52 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1515, 13407])).
% 2.33/2.52 tff(13409,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12386, 13408, 13400, 13398])).
% 2.33/2.52 tff(13410,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(13411,plain,
% 2.33/2.52 (~r(s(s(s(z))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13410, 13321, 12871, 13388, 12374])).
% 2.33/2.52 tff(13412,plain,
% 2.33/2.52 (b(s(s(s(z))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[7060, 13411])).
% 2.33/2.52 tff(13413,plain,
% 2.33/2.52 (~b(s(s(s(z))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[8573, 13412, 13386, 13383])).
% 2.33/2.52 tff(13414,plain,
% 2.33/2.52 (r(s(s(s(z))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12078, 13413])).
% 2.33/2.52 tff(13415,plain,
% 2.33/2.52 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11857, 13414, 13377])).
% 2.33/2.52 tff(13416,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12416, 13415])).
% 2.33/2.52 tff(13417,plain,
% 2.33/2.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13418,plain,
% 2.33/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(13419,plain,
% 2.33/2.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[13418, 13417])).
% 2.33/2.52 tff(13420,plain,
% 2.33/2.52 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13419, 141, 13414, 13377])).
% 2.33/2.52 tff(13421,plain,
% 2.33/2.52 (~r(s(s(s(z))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12601, 13420])).
% 2.33/2.52 tff(13422,plain,
% 2.33/2.52 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11873, 13421])).
% 2.33/2.52 tff(13423,plain,
% 2.33/2.52 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11866, 13422])).
% 2.33/2.52 tff(13424,plain,
% 2.33/2.52 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[13423, 12358])).
% 2.33/2.52 tff(13425,plain,
% 2.33/2.52 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13406, 245, 13424, 13416, 12871])).
% 2.33/2.52 tff(13426,plain,
% 2.33/2.52 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1515, 13425])).
% 2.33/2.52 tff(13427,plain,
% 2.33/2.52 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[13396, 245, 13424, 13416, 13321, 12871])).
% 2.33/2.52 tff(13428,plain,
% 2.33/2.52 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[809, 13427])).
% 2.33/2.52 tff(13429,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12386, 13428, 13426, 13414])).
% 2.33/2.52 tff(13430,plain,(b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(13431,plain,
% 2.33/2.52 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[12991, 13430])).
% 2.33/2.52 tff(13432,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~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(X0, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13433,plain,
% 2.33/2.52 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(13434,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[13433])).
% 2.33/2.52 tff(13435,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[13434, 13432])).
% 2.33/2.53 tff(13436,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(13437,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[13436, 13435])).
% 2.33/2.53 tff(13438,plain,
% 2.33/2.53 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13437, 245, 13431, 1943, 12363, 12355])).
% 2.33/2.53 tff(13439,plain,
% 2.33/2.53 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12714, 13438])).
% 2.33/2.53 tff(13440,plain,
% 2.33/2.53 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13050, 245, 13431, 1943, 12355])).
% 2.33/2.53 tff(13441,plain,
% 2.33/2.53 (r(z, s(s(s(s(s(s(z)))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13060, 13440])).
% 2.33/2.53 tff(13442,plain,
% 2.33/2.53 (b(elem!1, z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13099, 1943])).
% 2.33/2.53 tff(13443,plain,
% 2.33/2.53 (b(s(s(s(z))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[10863, 12360])).
% 2.33/2.53 tff(13444,plain,
% 2.33/2.53 ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11969, 13430])).
% 2.33/2.53 tff(13445,plain,
% 2.33/2.53 (~b(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13444, 13443, 13442])).
% 2.33/2.53 tff(13446,plain,
% 2.33/2.53 (r(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[7060, 13445])).
% 2.33/2.53 tff(13447,plain,
% 2.33/2.53 (((~![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(s(z))), 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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13448,plain,
% 2.33/2.53 (((~r(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))), z))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13449,plain,
% 2.33/2.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))), 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(s(z))), z)) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[13448])).
% 2.33/2.53 tff(13450,plain,
% 2.33/2.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))), 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(s(z))), z)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[13449, 13447])).
% 2.33/2.53 tff(13451,plain,
% 2.33/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))), z)))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(13452,plain,
% 2.33/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[13451, 13450])).
% 2.33/2.53 tff(13453,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13452, 141, 13446, 13441, 13439])).
% 2.33/2.53 tff(13454,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(z), elem!1)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(13455,plain,
% 2.33/2.53 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13454, 619, 11227])).
% 2.33/2.53 tff(13456,plain,
% 2.33/2.53 (r(s(s(s(s(elem!1)))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2558, 13455])).
% 2.33/2.53 tff(13457,plain,
% 2.33/2.53 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11232, 13456, 11227])).
% 2.33/2.53 tff(13458,plain,
% 2.33/2.53 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[738, 13457])).
% 2.33/2.53 tff(13459,plain,
% 2.33/2.53 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[8375, 141, 12241, 12248])).
% 2.33/2.53 tff(13460,plain,
% 2.33/2.53 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[809, 13459])).
% 2.33/2.53 tff(13461,plain,
% 2.33/2.53 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(elem!1))), z)),
% 2.33/2.53 inference(transitivity,[status(thm)],[12948, 11673])).
% 2.33/2.53 tff(13462,plain,
% 2.33/2.53 (r(s(s(s(elem!1))), z)),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[13456, 13461])).
% 2.33/2.53 tff(13463,plain,
% 2.33/2.53 (~r(s(z), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2109, 13462, 12180])).
% 2.33/2.53 tff(13464,plain,
% 2.33/2.53 (b(s(z), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[232, 13463])).
% 2.33/2.53 tff(13465,plain,
% 2.33/2.53 (~b(z, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12032, 13460, 13458, 13464])).
% 2.33/2.53 tff(13466,plain,
% 2.33/2.53 (r(z, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1421, 13465])).
% 2.33/2.53 tff(13467,plain,
% 2.33/2.53 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[4226, 13466, 13456])).
% 2.33/2.53 tff(13468,plain,
% 2.33/2.53 (b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[217, 13467])).
% 2.33/2.53 tff(13469,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13470,plain,
% 2.33/2.53 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13471,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[13470])).
% 2.33/2.53 tff(13472,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[13471, 13469])).
% 2.33/2.53 tff(13473,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(13474,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[13473, 13472])).
% 2.33/2.53 tff(13475,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13474, 245, 13464, 13431, 13468, 13460, 13458])).
% 2.33/2.53 tff(13476,plain,((~r(s(z), elem!1)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(13477,plain,
% 2.33/2.53 (~r(s(z), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13476, 11227])).
% 2.33/2.53 tff(13478,plain,
% 2.33/2.53 (b(s(z), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[10872, 13477])).
% 2.33/2.53 tff(13479,plain,
% 2.33/2.53 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12864, 13478])).
% 2.33/2.53 tff(13480,plain,
% 2.33/2.53 (b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[217, 9748])).
% 2.33/2.53 tff(13481,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13482,plain,
% 2.33/2.53 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13483,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[13482])).
% 2.33/2.53 tff(13484,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[13483, 13481])).
% 2.33/2.53 tff(13485,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(13486,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[13485, 13484])).
% 2.33/2.53 tff(13487,plain,
% 2.33/2.53 (~b(s(z), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13486, 245, 13431, 13480, 13479])).
% 2.33/2.53 tff(13488,plain,
% 2.33/2.53 (r(s(z), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[232, 13487])).
% 2.33/2.53 tff(13489,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11139, 141, 1449, 740, 997])).
% 2.33/2.53 tff(13490,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(13491,plain,
% 2.33/2.53 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13490, 740, 1449])).
% 2.33/2.53 tff(13492,plain,
% 2.33/2.53 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[809, 13491])).
% 2.33/2.53 tff(13493,plain,
% 2.33/2.53 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12794, 245, 13480, 3380, 13492])).
% 2.33/2.53 tff(13494,plain,
% 2.33/2.53 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12933, 32, 13493, 12367])).
% 2.33/2.53 tff(13495,plain,
% 2.33/2.53 (((~![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(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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13496,plain,
% 2.33/2.53 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13497,plain,
% 2.33/2.53 (((~![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(elem!1)))), s(s(s(s(s(z))))))) | (~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(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[13496])).
% 2.33/2.53 tff(13498,plain,
% 2.33/2.53 (((~![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(elem!1)))), s(s(s(s(s(z))))))) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[13497, 13495])).
% 2.33/2.53 tff(13499,plain,
% 2.33/2.53 ((~![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(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(13500,plain,
% 2.33/2.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[13499, 13498])).
% 2.33/2.53 tff(13501,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13500, 141, 106, 740, 13494])).
% 2.33/2.53 tff(13502,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(13503,plain,
% 2.33/2.53 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13502, 1449, 13479, 106])).
% 2.33/2.53 tff(13504,plain,
% 2.33/2.53 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[758, 13503])).
% 2.33/2.53 tff(13505,plain,
% 2.33/2.53 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11232, 106, 11227])).
% 2.33/2.53 tff(13506,plain,
% 2.33/2.53 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[738, 13505])).
% 2.33/2.53 tff(13507,plain,
% 2.33/2.53 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12637, 12568, 11227])).
% 2.33/2.53 tff(13508,plain,
% 2.33/2.53 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1515, 13507])).
% 2.33/2.53 tff(13509,plain,
% 2.33/2.53 (~b(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12534, 13508, 13506, 2222])).
% 2.33/2.53 tff(13510,plain,
% 2.33/2.53 (r(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[7060, 13509])).
% 2.33/2.53 tff(13511,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13225, 141, 106, 12568, 13510])).
% 2.33/2.53 tff(13512,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(13513,plain,
% 2.33/2.53 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13512, 13504, 106, 11227])).
% 2.33/2.53 tff(13514,plain,
% 2.33/2.53 (~r(s(s(s(z))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12601, 13513])).
% 2.33/2.53 tff(13515,plain,
% 2.33/2.53 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11873, 13514])).
% 2.33/2.53 tff(13516,plain,
% 2.33/2.53 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11866, 13515])).
% 2.33/2.53 tff(13517,plain,
% 2.33/2.53 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11844, 12358])).
% 2.33/2.53 tff(13518,assumption,(~b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.33/2.53 tff(13519,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13518, 13517])).
% 2.33/2.53 tff(13520,plain,((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(z))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(13521,plain,
% 2.33/2.53 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13520, 13516])).
% 2.33/2.53 tff(13522,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13523,plain,
% 2.33/2.53 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13524,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[13523])).
% 2.33/2.53 tff(13525,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.53 inference(transitivity,[status(thm)],[13524, 13522])).
% 2.33/2.53 tff(13526,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(13527,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[13526, 13525])).
% 2.33/2.53 tff(13528,plain,
% 2.33/2.53 (~b(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13527, 245, 13431, 13521, 13480, 13479])).
% 2.33/2.53 tff(13529,plain,
% 2.33/2.53 (r(s(s(s(z))), z)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[7060, 13528])).
% 2.33/2.53 tff(13530,plain,
% 2.33/2.53 (~b(s(s(s(z))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12520, 245, 13521, 13480, 13479])).
% 2.33/2.53 tff(13531,plain,
% 2.33/2.53 (r(s(s(s(z))), s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[12078, 13530])).
% 2.33/2.53 tff(13532,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[985, 13531, 13529, 13488])).
% 2.33/2.53 tff(13533,plain,((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(13534,plain,
% 2.33/2.53 (~r(z, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[13533, 106, 11227])).
% 2.33/2.53 tff(13535,plain,
% 2.33/2.53 (b(z, s(z))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1421, 13534])).
% 2.33/2.53 tff(13536,plain,
% 2.33/2.53 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(13537,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[13536])).
% 2.33/2.53 tff(13538,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[13537, 11202])).
% 2.33/2.53 tff(13539,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(13540,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13539, 13538])).
% 2.33/2.54 tff(13541,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13540, 245, 13431, 4187, 2653, 3380])).
% 2.33/2.54 tff(13542,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(13543,plain,
% 2.33/2.54 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13542, 13535, 13479])).
% 2.33/2.54 tff(13544,plain,
% 2.33/2.54 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[217, 13543])).
% 2.33/2.54 tff(13545,plain,
% 2.33/2.54 (~r(s(z), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[225, 13544, 106])).
% 2.33/2.54 tff(13546,plain,
% 2.33/2.54 (b(s(z), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[232, 13545])).
% 2.33/2.54 tff(13547,plain,
% 2.33/2.54 (b(z, s(elem!1))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13431, 13204])).
% 2.33/2.54 tff(13548,plain,
% 2.33/2.54 ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[4196, 13430, 13547])).
% 2.33/2.54 tff(13549,plain,
% 2.33/2.54 (~b(s(elem!1), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13548, 13546, 13535])).
% 2.33/2.54 tff(13550,plain,
% 2.33/2.54 (r(s(elem!1), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12447, 13549])).
% 2.33/2.54 tff(13551,plain,
% 2.33/2.54 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12032, 13546, 13506, 13535])).
% 2.33/2.54 tff(13552,plain,
% 2.33/2.54 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[809, 13551])).
% 2.33/2.54 tff(13553,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1003, 13552, 13550, 12242])).
% 2.33/2.54 tff(13554,plain,((~r(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(13555,plain,
% 2.33/2.54 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13554, 11227])).
% 2.33/2.54 tff(13556,plain,
% 2.33/2.54 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2558, 13555])).
% 2.33/2.54 tff(13557,plain,
% 2.33/2.54 (b(elem!1, z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13099, 13556])).
% 2.33/2.54 tff(13558,plain,
% 2.33/2.54 ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[4595, 13430])).
% 2.33/2.54 tff(13559,plain,
% 2.33/2.54 (~b(z, s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13558, 13557, 13478])).
% 2.33/2.54 tff(13560,plain,
% 2.33/2.54 (r(z, s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1421, 13559])).
% 2.33/2.54 tff(13561,plain,
% 2.33/2.54 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13120, 13431])).
% 2.33/2.54 tff(13562,plain,
% 2.33/2.54 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13561, 13560, 13479, 13556])).
% 2.33/2.54 tff(13563,plain,
% 2.33/2.54 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12354, 13562])).
% 2.33/2.54 tff(13564,plain,
% 2.33/2.54 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12347, 13563])).
% 2.33/2.54 tff(13565,plain,
% 2.33/2.54 (r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12326, 13564])).
% 2.33/2.54 tff(13566,plain,
% 2.33/2.54 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12257, 141, 12241, 13565])).
% 2.33/2.54 tff(13567,plain,
% 2.33/2.54 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12288, 32, 12285, 13566])).
% 2.33/2.54 tff(13568,plain,
% 2.33/2.54 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12752, 13565, 12241])).
% 2.33/2.54 tff(13569,plain,
% 2.33/2.54 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12758, 13568])).
% 2.33/2.54 tff(13570,plain,
% 2.33/2.54 ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[7253, 13430])).
% 2.33/2.54 tff(13571,plain,
% 2.33/2.54 (~b(s(s(s(z))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13570, 13557, 13478])).
% 2.33/2.54 tff(13572,plain,
% 2.33/2.54 (r(s(s(s(z))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[10863, 13571])).
% 2.33/2.54 tff(13573,plain,
% 2.33/2.54 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12601, 13572])).
% 2.33/2.54 tff(13574,plain,
% 2.33/2.54 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12637, 13573, 11227])).
% 2.33/2.54 tff(13575,plain,
% 2.33/2.54 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1515, 13574])).
% 2.33/2.54 tff(13576,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(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)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(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)))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13577,plain,
% 2.33/2.54 (((~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(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(z))))))) | (~b(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(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)))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13578,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(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))))))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[13577])).
% 2.33/2.54 tff(13579,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(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)))))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[13578, 13576])).
% 2.33/2.54 tff(13580,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(13581,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13580, 13579])).
% 2.33/2.54 tff(13582,plain,
% 2.33/2.54 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13581, 245, 13575, 13569, 13567])).
% 2.33/2.54 tff(13583,plain,
% 2.33/2.54 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12714, 13582])).
% 2.33/2.54 tff(13584,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13139, 141, 13573, 13583, 13565])).
% 2.33/2.54 tff(13585,plain,(b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(13586,plain,
% 2.33/2.54 (b(s(s(s(s(s(z))))), elem!1)),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13585, 12237])).
% 2.33/2.54 tff(13587,plain,
% 2.33/2.54 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(commutativity,[status(thm)],[])).
% 2.33/2.54 tff(13588,plain,
% 2.33/2.54 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 2.33/2.54 inference(symmetry,[status(thm)],[13587])).
% 2.33/2.54 tff(13589,plain,
% 2.33/2.54 ((~(s(z) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(z)))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[13588])).
% 2.33/2.54 tff(13590,plain,
% 2.33/2.54 (~(s(s(s(s(s(s(z)))))) = s(z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[12303, 13589])).
% 2.33/2.54 tff(13591,plain,
% 2.33/2.54 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13050, 245, 13431, 1943, 12699])).
% 2.33/2.54 tff(13592,plain,
% 2.33/2.54 (r(z, s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13060, 13591])).
% 2.33/2.54 tff(13593,plain,
% 2.33/2.54 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13067, 245, 13431, 1943, 13585, 12699])).
% 2.33/2.54 tff(13594,plain,
% 2.33/2.54 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12758, 13593])).
% 2.33/2.54 tff(13595,plain,
% 2.33/2.54 (~b(z, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12998, 245, 13431, 1943, 13585])).
% 2.33/2.54 tff(13596,plain,
% 2.33/2.54 (r(z, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[758, 13595])).
% 2.33/2.54 tff(13597,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13075, 141, 13596, 13594, 13592])).
% 2.33/2.54 tff(13598,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(13599,plain,
% 2.33/2.54 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13598, 1943])).
% 2.33/2.54 tff(13600,plain,
% 2.33/2.54 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12354, 13599])).
% 2.33/2.54 tff(13601,plain,
% 2.33/2.54 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12347, 13600])).
% 2.33/2.54 tff(13602,plain,
% 2.33/2.54 (r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12326, 13601])).
% 2.33/2.54 tff(13603,plain,
% 2.33/2.54 (((~![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(s(z)))))), s(z))) | (~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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13604,plain,
% 2.33/2.54 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13605,plain,
% 2.33/2.54 (((~![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(s(z)))))), s(s(s(s(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), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[13604])).
% 2.33/2.54 tff(13606,plain,
% 2.33/2.54 (((~![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(s(z)))))), s(s(s(s(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), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[13605, 13603])).
% 2.33/2.54 tff(13607,plain,
% 2.33/2.54 ((~![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(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(13608,plain,
% 2.33/2.54 ((~![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(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13607, 13606])).
% 2.33/2.54 tff(13609,plain,
% 2.33/2.54 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13608, 141, 13602, 12290])).
% 2.33/2.54 tff(13610,plain,
% 2.33/2.54 (((~![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)))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13611,plain,
% 2.33/2.54 ((~![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)))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(13612,plain,
% 2.33/2.54 ((~![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))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13611, 13610])).
% 2.33/2.54 tff(13613,plain,
% 2.33/2.54 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13612, 32, 13609])).
% 2.33/2.54 tff(13614,plain,
% 2.33/2.54 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13613, 13590])).
% 2.33/2.54 tff(13615,plain,
% 2.33/2.54 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12296, 141, 13602, 12290])).
% 2.33/2.54 tff(13616,plain,
% 2.33/2.54 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12308, 13615])).
% 2.33/2.54 tff(13617,plain,
% 2.33/2.54 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13618,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[13617])).
% 2.33/2.54 tff(13619,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.54 inference(transitivity,[status(thm)],[13618, 9639])).
% 2.33/2.54 tff(13620,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(13621,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13620, 13619])).
% 2.33/2.54 tff(13622,plain,
% 2.33/2.54 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13621, 245, 13431, 1943, 13585])).
% 2.33/2.54 tff(13623,plain,
% 2.33/2.54 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[738, 13622])).
% 2.33/2.54 tff(13624,plain,
% 2.33/2.54 (~r(s(z), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13176, 13623])).
% 2.33/2.54 tff(13625,plain,
% 2.33/2.54 (b(s(z), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[232, 13624])).
% 2.33/2.54 tff(13626,plain,
% 2.33/2.54 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[8503, 245, 13625, 13431, 1943])).
% 2.33/2.54 tff(13627,plain,
% 2.33/2.54 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[217, 13626])).
% 2.33/2.54 tff(13628,plain,
% 2.33/2.54 (~b(s(elem!1), s(z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13626, 11611])).
% 2.33/2.54 tff(13629,plain,
% 2.33/2.54 (r(s(elem!1), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12447, 13628])).
% 2.33/2.54 tff(13630,plain,
% 2.33/2.54 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[10651])).
% 2.33/2.54 tff(13631,plain,
% 2.33/2.54 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.33/2.54 inference(symmetry,[status(thm)],[13630])).
% 2.33/2.54 tff(13632,plain,
% 2.33/2.54 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[12232])).
% 2.33/2.54 tff(13633,plain,
% 2.33/2.54 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[10660])).
% 2.33/2.54 tff(13634,plain,
% 2.33/2.54 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[13633, 13632, 13631])).
% 2.33/2.54 tff(13635,plain,
% 2.33/2.54 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[12233])).
% 2.33/2.54 tff(13636,plain,
% 2.33/2.54 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(symmetry,[status(thm)],[13635])).
% 2.33/2.54 tff(13637,plain,
% 2.33/2.54 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[11010, 13636])).
% 2.33/2.54 tff(13638,plain,
% 2.33/2.54 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[13637])).
% 2.33/2.54 tff(13639,plain,
% 2.33/2.54 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13608, 141, 12254, 12290])).
% 2.33/2.54 tff(13640,plain,
% 2.33/2.54 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13612, 32, 13639])).
% 2.33/2.54 tff(13641,plain,
% 2.33/2.54 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13640, 13590])).
% 2.33/2.54 tff(13642,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(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(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13643,plain,
% 2.33/2.54 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(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(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13644,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[13643])).
% 2.33/2.54 tff(13645,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[13644, 13642])).
% 2.33/2.54 tff(13646,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(13647,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[13646, 13645])).
% 2.33/2.54 tff(13648,plain,
% 2.33/2.54 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[13647, 245, 13178, 4187, 13641])).
% 2.33/2.54 tff(13649,plain,
% 2.33/2.54 (r(s(s(s(s(s(s(z)))))), z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[12742, 32, 12280, 13648])).
% 2.33/2.54 tff(13650,plain,
% 2.33/2.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(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(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13651,plain,
% 2.33/2.54 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(13652,plain,
% 2.33/2.54 (((~![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(s(s(z))))), z)) | (~r(s(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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[13651])).
% 2.33/2.54 tff(13653,plain,
% 2.33/2.54 (((~![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(s(s(z))))), z)) | (~r(s(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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.33/2.54 inference(transitivity,[status(thm)],[13652, 13650])).
% 2.33/2.55 tff(13654,plain,
% 2.33/2.55 ((~![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(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(13655,plain,
% 2.33/2.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13654, 13653])).
% 2.33/2.55 tff(13656,plain,
% 2.33/2.55 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13655, 141, 722, 13649])).
% 2.33/2.55 tff(13657,plain,
% 2.33/2.55 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[12758, 13656])).
% 2.33/2.55 tff(13658,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z)))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13659,plain,
% 2.33/2.55 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(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(s(s(z))))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z)))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13660,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z))))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13659])).
% 2.33/2.55 tff(13661,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z)))))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13660, 13658])).
% 2.33/2.55 tff(13662,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(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(s(s(z)))))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(13663,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z))))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13662, 13661])).
% 2.33/2.55 tff(13664,plain,
% 2.33/2.55 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13663, 245, 13178, 13431, 13585, 13641])).
% 2.33/2.55 tff(13665,plain,
% 2.33/2.55 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13664, 13657])).
% 2.33/2.55 tff(13666,plain,
% 2.33/2.55 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[809, 13665])).
% 2.33/2.55 tff(13667,plain,
% 2.33/2.55 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11744, 141, 219, 13666])).
% 2.33/2.55 tff(13668,plain,
% 2.33/2.55 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13667, 13638])).
% 2.33/2.55 tff(13669,plain,
% 2.33/2.55 (b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11051, 13668])).
% 2.33/2.55 tff(13670,plain,
% 2.33/2.55 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[10651])).
% 2.33/2.55 tff(13671,plain,
% 2.33/2.55 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13670, 1305])).
% 2.33/2.55 tff(13672,plain,
% 2.33/2.55 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.33/2.55 inference(symmetry,[status(thm)],[13671])).
% 2.33/2.55 tff(13673,plain,
% 2.33/2.55 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.33/2.55 inference(monotonicity,[status(thm)],[10656])).
% 2.33/2.55 tff(13674,plain,
% 2.33/2.55 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13673, 61])).
% 2.33/2.55 tff(13675,plain,
% 2.33/2.55 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.33/2.55 inference(symmetry,[status(thm)],[13674])).
% 2.33/2.55 tff(13676,plain,
% 2.33/2.55 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13675, 13672, 1940])).
% 2.33/2.55 tff(13677,plain,
% 2.33/2.55 (s(elem!1) = s(s(s(elem!1)))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[12232, 13676])).
% 2.33/2.55 tff(13678,plain,
% 2.33/2.55 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[4186, 1945])).
% 2.33/2.55 tff(13679,plain,
% 2.33/2.55 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[199])).
% 2.33/2.55 tff(13680,plain,
% 2.33/2.55 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.55 inference(symmetry,[status(thm)],[13679])).
% 2.33/2.55 tff(13681,plain,
% 2.33/2.55 (s(s(s(elem!1))) = s(elem!1)),
% 2.33/2.55 inference(symmetry,[status(thm)],[7113])).
% 2.33/2.55 tff(13682,plain,
% 2.33/2.55 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13681])).
% 2.33/2.55 tff(13683,plain,
% 2.33/2.55 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 2.33/2.55 inference(transitivity,[status(thm)],[312, 255, 13682, 49])).
% 2.33/2.55 tff(13684,plain,
% 2.33/2.55 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13683])).
% 2.33/2.55 tff(13685,plain,
% 2.33/2.55 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13684, 13680])).
% 2.33/2.55 tff(13686,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))), introduced(assumption)).
% 2.33/2.55 tff(13687,plain,
% 2.33/2.55 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13686, 13685])).
% 2.33/2.55 tff(13688,plain,
% 2.33/2.55 (~b(s(s(s(z))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11359, 13687, 2197, 13678])).
% 2.33/2.55 tff(13689,plain,
% 2.33/2.55 (r(s(s(s(z))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[7060, 13688])).
% 2.33/2.55 tff(13690,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[12978, 141, 722, 13689])).
% 2.33/2.55 tff(13691,plain,
% 2.33/2.55 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1515, 13690])).
% 2.33/2.55 tff(13692,plain,
% 2.33/2.55 (b(elem!1, s(s(s(z))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13686, 13684])).
% 2.33/2.55 tff(13693,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~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(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13694,plain,
% 2.33/2.55 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13695,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13694])).
% 2.33/2.55 tff(13696,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13695, 13693])).
% 2.33/2.55 tff(13697,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(13698,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13697, 13696])).
% 2.33/2.55 tff(13699,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13698, 245, 4186, 13692, 5823, 4878, 13691])).
% 2.33/2.55 tff(13700,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~(s(elem!1) = s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(13701,plain,
% 2.33/2.55 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13700, 12381, 13677])).
% 2.33/2.55 tff(13702,plain,
% 2.33/2.55 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13701, 13431])).
% 2.33/2.55 tff(13703,plain,
% 2.33/2.55 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13702, 13669, 4186, 13586, 722])).
% 2.33/2.55 tff(13704,plain,
% 2.33/2.55 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(commutativity,[status(thm)],[])).
% 2.33/2.55 tff(13705,plain,
% 2.33/2.55 (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[1563, 13704])).
% 2.33/2.55 tff(13706,assumption,(~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.33/2.55 tff(13707,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13706, 13705])).
% 2.33/2.55 tff(13708,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(13709,plain,
% 2.33/2.55 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13708, 10861])).
% 2.33/2.55 tff(13710,plain,
% 2.33/2.55 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1630, 13709])).
% 2.33/2.55 tff(13711,plain,
% 2.33/2.55 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13710, 13703])).
% 2.33/2.55 tff(13712,plain,
% 2.33/2.55 (r(s(elem!1), s(s(s(z))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13711, 13634])).
% 2.33/2.55 tff(13713,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[8551, 13712, 998])).
% 2.33/2.55 tff(13714,plain,
% 2.33/2.55 (b(s(s(s(z))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[12078, 13713])).
% 2.33/2.55 tff(13715,plain,
% 2.33/2.55 (~b(s(s(s(z))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[8573, 13714, 4187, 13178])).
% 2.33/2.55 tff(13716,plain,
% 2.33/2.55 (r(s(s(s(z))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[7060, 13715])).
% 2.33/2.55 tff(13717,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[7090, 13716, 740])).
% 2.33/2.55 tff(13718,plain,
% 2.33/2.55 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1515, 13717])).
% 2.33/2.55 tff(13719,plain,
% 2.33/2.55 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[12933, 32, 12367, 13667])).
% 2.33/2.55 tff(13720,plain,
% 2.33/2.55 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13218, 245, 13718, 13585, 13719])).
% 2.33/2.55 tff(13721,plain,
% 2.33/2.55 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13520, 13720])).
% 2.33/2.55 tff(13722,plain,
% 2.33/2.55 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11866, 13721])).
% 2.33/2.55 tff(13723,plain,
% 2.33/2.55 (r(s(s(s(z))), elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11873, 13722])).
% 2.33/2.55 tff(13724,plain,
% 2.33/2.55 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[12601, 13723])).
% 2.33/2.55 tff(13725,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), 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))))) | (~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(X0, 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(z), 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))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13726,plain,
% 2.33/2.55 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13727,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, 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(z), 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))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13726])).
% 2.33/2.55 tff(13728,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, 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(z), 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))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13727, 13725])).
% 2.33/2.55 tff(13729,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(13730,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13729, 13728])).
% 2.33/2.55 tff(13731,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13730, 245, 6123, 955, 12309, 13030, 13021])).
% 2.33/2.55 tff(13732,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(13733,plain,
% 2.33/2.55 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13732, 13724, 12254, 12290, 13718])).
% 2.33/2.55 tff(13734,plain,
% 2.33/2.55 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[909, 13733])).
% 2.33/2.55 tff(13735,plain,
% 2.33/2.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13736,plain,
% 2.33/2.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(13737,plain,
% 2.33/2.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13736, 13735])).
% 2.33/2.55 tff(13738,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13737, 141, 13734, 722, 13716])).
% 2.33/2.55 tff(13739,plain,((~b(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))) | (~b(elem!1, z)) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(13740,plain,
% 2.33/2.55 (~b(z, s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13739, 13623, 13602, 12290, 13596, 13629, 13442, 13627])).
% 2.33/2.55 tff(13741,plain,
% 2.33/2.55 (r(z, s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[1421, 13740])).
% 2.33/2.55 tff(13742,plain,
% 2.33/2.55 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[12466, 13741, 13585, 1943])).
% 2.33/2.55 tff(13743,plain,
% 2.33/2.55 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[809, 13742])).
% 2.33/2.55 tff(13744,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), 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(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13745,plain,
% 2.33/2.55 (((~b(s(s(s(s(s(s(z)))))), 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(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(s(z)))))))) <=> ((~b(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(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13746,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13745])).
% 2.33/2.55 tff(13747,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13746, 13744])).
% 2.33/2.55 tff(13748,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z))))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(13749,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13748, 13747])).
% 2.33/2.55 tff(13750,plain,
% 2.33/2.55 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13749, 245, 13743, 13616, 13614])).
% 2.33/2.55 tff(13751,plain,
% 2.33/2.55 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[12288, 32, 12285, 13750])).
% 2.33/2.55 tff(13752,plain,
% 2.33/2.55 (((~![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(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(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13753,plain,
% 2.33/2.55 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13754,plain,
% 2.33/2.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, 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(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13753])).
% 2.33/2.55 tff(13755,plain,
% 2.33/2.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, 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(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[13754, 13752])).
% 2.33/2.55 tff(13756,plain,
% 2.33/2.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(13757,plain,
% 2.33/2.55 ((~![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(z, s(s(s(s(s(s(z))))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[13756, 13755])).
% 2.33/2.55 tff(13758,plain,
% 2.33/2.55 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13757, 141, 13596, 13751])).
% 2.33/2.55 tff(13759,plain,
% 2.33/2.55 (b(z, s(s(s(s(s(s(z)))))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[13060, 13758])).
% 2.33/2.55 tff(13760,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13761,plain,
% 2.33/2.55 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z))) <=> ((~b(s(z), 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)))))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(13762,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(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(X0, 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(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[13761])).
% 2.33/2.55 tff(13763,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(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(X0, 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(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[13762, 13760])).
% 2.33/2.56 tff(13764,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(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)))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(13765,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13764, 13763])).
% 2.33/2.56 tff(13766,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13765, 245, 13625, 13759, 13616, 13614])).
% 2.33/2.56 tff(13767,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(13768,plain,
% 2.33/2.56 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13767, 12248])).
% 2.33/2.56 tff(13769,plain,
% 2.33/2.56 (r(s(s(s(s(elem!1)))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2558, 13768])).
% 2.33/2.56 tff(13770,plain,
% 2.33/2.56 (r(elem!1, z)),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13769, 12948])).
% 2.33/2.56 tff(13771,plain,
% 2.33/2.56 (r(s(s(s(elem!1))), z)),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13769, 13461])).
% 2.33/2.56 tff(13772,plain,
% 2.33/2.56 (~r(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2109, 13771, 12180])).
% 2.33/2.56 tff(13773,plain,
% 2.33/2.56 (b(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[232, 13772])).
% 2.33/2.56 tff(13774,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13775,plain,
% 2.33/2.56 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13776,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[13775])).
% 2.33/2.56 tff(13777,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[13776, 13774])).
% 2.33/2.56 tff(13778,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(13779,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13778, 13777])).
% 2.33/2.56 tff(13780,plain,
% 2.33/2.56 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13779, 245, 13773, 13431, 2653, 13585])).
% 2.33/2.56 tff(13781,plain,
% 2.33/2.56 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[809, 13780])).
% 2.33/2.56 tff(13782,plain,
% 2.33/2.56 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13237, 13781, 619, 13769])).
% 2.33/2.56 tff(13783,plain,
% 2.33/2.56 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[738, 13782])).
% 2.33/2.56 tff(13784,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13785,plain,
% 2.33/2.56 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13786,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[13785])).
% 2.33/2.56 tff(13787,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.56 inference(transitivity,[status(thm)],[13786, 13784])).
% 2.33/2.56 tff(13788,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(13789,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13788, 13787])).
% 2.33/2.56 tff(13790,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13789, 245, 13773, 13431, 2653, 13783, 13585])).
% 2.33/2.56 tff(13791,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(13792,plain,
% 2.33/2.56 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13791, 619])).
% 2.33/2.56 tff(13793,plain,
% 2.33/2.56 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[217, 13792])).
% 2.33/2.56 tff(13794,plain,
% 2.33/2.56 (~r(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[4226, 13793, 13769])).
% 2.33/2.56 tff(13795,plain,
% 2.33/2.56 (b(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1421, 13794])).
% 2.33/2.56 tff(13796,plain,
% 2.33/2.56 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11744, 141, 13793, 997])).
% 2.33/2.56 tff(13797,plain,
% 2.33/2.56 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12933, 32, 12367, 13796])).
% 2.33/2.56 tff(13798,plain,
% 2.33/2.56 (~r(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13237, 997, 619, 13769])).
% 2.33/2.56 tff(13799,plain,
% 2.33/2.56 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[738, 13798])).
% 2.33/2.56 tff(13800,plain,
% 2.33/2.56 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13796, 13638])).
% 2.33/2.56 tff(13801,plain,
% 2.33/2.56 (b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11051, 13800])).
% 2.33/2.56 tff(13802,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13227, 13801, 13585, 13769, 13586, 13773, 619])).
% 2.33/2.56 tff(13803,plain,
% 2.33/2.56 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1515, 13802])).
% 2.33/2.56 tff(13804,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12386, 13803, 997])).
% 2.33/2.56 tff(13805,plain,
% 2.33/2.56 (b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12078, 13804])).
% 2.33/2.56 tff(13806,plain,
% 2.33/2.56 (~b(s(s(s(z))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8573, 13805, 13795, 13773])).
% 2.33/2.56 tff(13807,plain,
% 2.33/2.56 (r(s(s(s(z))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[7060, 13806])).
% 2.33/2.56 tff(13808,plain,
% 2.33/2.56 (~r(z, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[7090, 13807, 13803])).
% 2.33/2.56 tff(13809,plain,
% 2.33/2.56 (b(z, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[758, 13808])).
% 2.33/2.56 tff(13810,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13811,plain,
% 2.33/2.56 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13812,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[13811])).
% 2.33/2.56 tff(13813,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[13812, 13810])).
% 2.33/2.56 tff(13814,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(13815,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13814, 13813])).
% 2.33/2.56 tff(13816,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13815, 245, 13431, 13809, 13799, 13797])).
% 2.33/2.56 tff(13817,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(13818,plain,
% 2.33/2.56 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13817, 619])).
% 2.33/2.56 tff(13819,plain,
% 2.33/2.56 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[809, 13818])).
% 2.33/2.56 tff(13820,plain,
% 2.33/2.56 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12032, 13819, 13773, 13795])).
% 2.33/2.56 tff(13821,plain,
% 2.33/2.56 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[738, 13820])).
% 2.33/2.56 tff(13822,plain,
% 2.33/2.56 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[731, 13821, 13770])).
% 2.33/2.56 tff(13823,plain,
% 2.33/2.56 (b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11051, 13822])).
% 2.33/2.56 tff(13824,plain,
% 2.33/2.56 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13823, 12235])).
% 2.33/2.56 tff(13825,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13227, 13823, 13585, 13769, 13586, 13773, 619])).
% 2.33/2.56 tff(13826,plain,
% 2.33/2.56 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1515, 13825])).
% 2.33/2.56 tff(13827,plain,
% 2.33/2.56 (~r(s(s(s(z))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12980, 13826, 13821])).
% 2.33/2.56 tff(13828,plain,
% 2.33/2.56 (b(s(s(s(z))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[7060, 13827])).
% 2.33/2.56 tff(13829,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8573, 13828, 13795, 13773])).
% 2.33/2.56 tff(13830,plain,
% 2.33/2.56 (r(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12078, 13829])).
% 2.33/2.56 tff(13831,plain,
% 2.33/2.56 (~r(s(s(s(z))), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8430, 13830, 619])).
% 2.33/2.56 tff(13832,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11873, 13831])).
% 2.33/2.56 tff(13833,plain,
% 2.33/2.56 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11866, 13832])).
% 2.33/2.56 tff(13834,plain,
% 2.33/2.56 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13520, 13833])).
% 2.33/2.56 tff(13835,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13836,plain,
% 2.33/2.56 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13837,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[13836])).
% 2.33/2.56 tff(13838,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[13837, 13835])).
% 2.33/2.56 tff(13839,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(13840,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13839, 13838])).
% 2.33/2.56 tff(13841,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13840, 245, 13431, 13834, 13828, 13585, 13824])).
% 2.33/2.56 tff(13842,plain,(~r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(13843,plain,
% 2.33/2.56 (b(s(z), elem!1)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10872, 13842])).
% 2.33/2.56 tff(13844,plain,
% 2.33/2.56 ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[7284, 13430])).
% 2.33/2.56 tff(13845,plain,
% 2.33/2.56 (~b(elem!1, z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13844, 13843, 13586])).
% 2.33/2.56 tff(13846,plain,
% 2.33/2.56 (r(elem!1, z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10943, 13845])).
% 2.33/2.56 tff(13847,plain,
% 2.33/2.56 (r(s(s(s(elem!1))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11676, 13846])).
% 2.33/2.56 tff(13848,plain,
% 2.33/2.56 ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6835, 13430])).
% 2.33/2.56 tff(13849,plain,
% 2.33/2.56 (~b(elem!1, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13848, 13843, 13586])).
% 2.33/2.56 tff(13850,plain,
% 2.33/2.56 (~b(s(s(s(elem!1))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10734, 13849])).
% 2.33/2.56 tff(13851,plain,
% 2.33/2.56 (r(s(s(s(elem!1))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[265, 13850])).
% 2.33/2.56 tff(13852,plain,
% 2.33/2.56 (~r(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1457, 13851, 13847])).
% 2.33/2.56 tff(13853,plain,
% 2.33/2.56 (b(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[1421, 13852])).
% 2.33/2.56 tff(13854,plain,
% 2.33/2.56 (~r(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2177, 13851, 13847])).
% 2.33/2.56 tff(13855,plain,
% 2.33/2.56 (b(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[232, 13854])).
% 2.33/2.56 tff(13856,plain,
% 2.33/2.56 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12032, 13855, 13853])).
% 2.33/2.56 tff(13857,plain,
% 2.33/2.56 (~b(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13856, 709])).
% 2.33/2.56 tff(13858,plain,
% 2.33/2.56 (r(s(s(s(s(s(z))))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[738, 13857])).
% 2.33/2.56 tff(13859,plain,
% 2.33/2.56 ((~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[731, 13846])).
% 2.33/2.56 tff(13860,plain,
% 2.33/2.56 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[13859, 13858])).
% 2.33/2.56 tff(13861,plain,
% 2.33/2.56 (b(elem!1, s(s(s(s(s(z))))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11051, 13860])).
% 2.33/2.56 tff(13862,plain,
% 2.33/2.56 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[13861, 12235])).
% 2.33/2.56 tff(13863,plain,
% 2.33/2.56 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[12864, 13843])).
% 2.33/2.56 tff(13864,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13865,plain,
% 2.33/2.56 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(13866,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[13865])).
% 2.33/2.56 tff(13867,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[13866, 13864])).
% 2.33/2.57 tff(13868,plain,
% 2.33/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(13869,plain,
% 2.33/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[13868, 13867])).
% 2.33/2.57 tff(13870,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[13869, 245, 13863, 709, 13585, 13862])).
% 2.33/2.57 tff(13871,plain,(~b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(13872,plain,
% 2.33/2.57 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[809, 13871])).
% 2.33/2.57 tff(13873,plain,
% 2.33/2.57 (r(elem!1, s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[10716, 13849])).
% 2.33/2.57 tff(13874,plain,
% 2.33/2.57 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[13376, 13873])).
% 2.33/2.57 tff(13875,plain,
% 2.33/2.57 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11744, 141, 13874, 13872])).
% 2.33/2.57 tff(13876,plain,
% 2.33/2.57 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[12933, 32, 12367, 13875])).
% 2.33/2.57 tff(13877,plain,
% 2.33/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(13878,plain,
% 2.33/2.57 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(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(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(13879,plain,
% 2.33/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[13878])).
% 2.33/2.57 tff(13880,plain,
% 2.33/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[13879, 13877])).
% 2.33/2.57 tff(13881,plain,
% 2.33/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(13882,plain,
% 2.33/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[13881, 13880])).
% 2.33/2.57 tff(13883,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[13882, 245, 13431, 13853, 13863, 13585, 13876])).
% 2.33/2.57 % SZS output end Proof
% 2.33/2.57 % E exiting
%------------------------------------------------------------------------------